(3x+4)(3x+4)-(5x-6)(5x-6)=0

Solution for (3x+4)(3x+4)-(5x-6)(5x-6)=0 equation:

(3x+4)(3x+4)-(5x-6)(5x-6)=0

We multiply parentheses ..

(+9x^2+12x+12x+16)-(5x-6)(5x-6)=0

We get rid of parentheses

9x^2+12x+12x-(5x-6)(5x-6)+16=0

We multiply parentheses ..

9x^2-(+25x^2-30x-30x+36)+12x+12x+16=0

We add all the numbers together, and all the variables

9x^2-(+25x^2-30x-30x+36)+24x+16=0

We get rid of parentheses

9x^2-25x^2+30x+30x+24x-36+16=0

We add all the numbers together, and all the variables

-16x^2+84x-20=0

a = -16; b = 84; c = -20;
Δ = b2-4ac
Δ = 842-4·(-16)·(-20)
Δ = 5776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5776}=76$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-76}{2*-16}=\frac{-160}{-32}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+76}{2*-16}=\frac{-8}{-32}
=1/4
$