How to find the point(s) when two plot curves cross?

Hello. I want to plot these 2 plots:

y_1=a*x+b;

y_2=a*(x^2);

and find to point where they meet? The exact values of x. This is my code so far, but I don't know how to finish the statement :

clc;
clear all;  

a=5;
b=10;
x=linspace(0,10,50);
y_1=a*x+b;
y_2=(x.^2);
for i=1:length(x);
    if(a*x+b==(x.^2));
        printf(x)
    end      
end

plot(y_1);
hold on;
plot(y_2);

Answer 1

[Image Analyst]

Use roots():

a=5;
b=10;
x=linspace(-4,10,50);
y_1=a*x+b;
y_2=(x.^2);

for i=1:length(x)
      if(a*x+b==(x.^2))
          printf(x)
    end
end

plot(x, y_1,'b-', 'LineWidth', 2);
hold on;
plot(x, y_2),'c-', 'LineWidth', 2;
grid on;

xRoots = roots([1, -a, -b])

y1 = a * xRoots(1) + b;
y2 = a * xRoots(2) + b;
plot(xRoots, [y1, y2],'ro', 'LineWidth', 2, 'MarkerSize', 13);

[tomer polsky]

hi I tried what you said :

for i=1:length(x)
      if(a*x+b==(x.^2))
          printf(x)
    end
end

but i did not get x why ?

[Image Analyst]

I never said to do that and I never would. I know better. Checking for equality is tricky with floating point numbers. See the FAQ: https://matlab.wikia.com/wiki/FAQ#Why_is_0.3_-_0.2_-_0.1_.28or_similar.29_not_equal_to_zero.3F

[tomer polsky]

ok lets so that matlab cant handle do equality with floating numbers . but if I represnt x as x=1:1:50 means that that there are not floating numbers .

and my question is there any way with out using roots command to find when y_1==y_2?

[Image Analyst]

You can use ismembertol() like the FAQ says, but why? What's wrong with using roots? Why deny yourself the simplest, one-line solution? Usually people don't ask and prefer to do things the more complicated less accurate way so I'm not sure why you do.