(-4x-5)(-4x+5)=(4x-3)2

Solution for (-4x-5)(-4x+5)=(4x-3)2 equation:

(-4x-5)(-4x+5)=(4x-3)2

We move all terms to the left:

(-4x-5)(-4x+5)-((4x-3)2)=0

We multiply parentheses ..

(+16x^2-20x+20x-25)-((4x-3)2)=0


We calculate terms in parentheses: -((4x-3)2), so:

(4x-3)2

We multiply parentheses

8x-6

Back to the equation:

-(8x-6)


We get rid of parentheses

16x^2-20x+20x-8x-25+6=0

We add all the numbers together, and all the variables

16x^2-8x-19=0

a = 16; b = -8; c = -19;
Δ = b2-4ac
Δ = -82-4·16·(-19)
Δ = 1280
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:

$\sqrt{\Delta}=\sqrt{1280}=\sqrt{256*5}=\sqrt{256}*\sqrt{5}=16\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-16\sqrt{5}}{2*16}=\frac{8-16\sqrt{5}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+16\sqrt{5}}{2*16}=\frac{8+16\sqrt{5}}{32}
$