x(4x-4)=15

Solution for x(4x-4)=15 equation:

x(4x-4)=15

We move all terms to the left:

x(4x-4)-(15)=0

We multiply parentheses

4x^2-4x-15=0

a = 4; b = -4; c = -15;
Δ = b2-4ac
Δ = -42-4·4·(-15)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-16}{2*4}=\frac{-12}{8}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+16}{2*4}=\frac{20}{8}
=2+1/2
$