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

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

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

We multiply parentheses ..

(+9x^2+15x+15x+25)-(4x-3)(4x-3)=0

We get rid of parentheses

9x^2+15x+15x-(4x-3)(4x-3)+25=0

We multiply parentheses ..

9x^2-(+16x^2-12x-12x+9)+15x+15x+25=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-7x^2+54x+16=0

a = -7; b = 54; c = +16;
Δ = b2-4ac
Δ = 542-4·(-7)·16
Δ = 3364
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3364}=58$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-58}{2*-7}=\frac{-112}{-14}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+58}{2*-7}=\frac{4}{-14}
=-2/7
$