7x^2+5x=5x^2+13x+13

Solution for 7x^2+5x=5x^2+13x+13 equation:

7x^2+5x=5x^2+13x+13

We move all terms to the left:

7x^2+5x-(5x^2+13x+13)=0

We get rid of parentheses

7x^2-5x^2+5x-13x-13=0

We add all the numbers together, and all the variables

2x^2-8x-13=0

a = 2; b = -8; c = -13;
Δ = b2-4ac
Δ = -82-4·2·(-13)
Δ = 168
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{42}}{2*2}=\frac{8-2\sqrt{42}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{42}}{2*2}=\frac{8+2\sqrt{42}}{4}
$