x=2(x-1)(2x-3)=15

Solution for x=2(x-1)(2x-3)=15 equation:

x=2(x-1)(2x-3)=15

We move all terms to the left:

x-(2(x-1)(2x-3))=0

We multiply parentheses ..

-(2(+2x^2-3x-2x+3))+x=0


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

2(+2x^2-3x-2x+3)

We multiply parentheses

4x^2-6x-4x+6

We add all the numbers together, and all the variables

4x^2-10x+6

Back to the equation:

-(4x^2-10x+6)


We add all the numbers together, and all the variables

x-(4x^2-10x+6)=0

We get rid of parentheses

-4x^2+x+10x-6=0

We add all the numbers together, and all the variables

-4x^2+11x-6=0

a = -4; b = 11; c = -6;
Δ = b2-4ac
Δ = 112-4·(-4)·(-6)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-5}{2*-4}=\frac{-16}{-8}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+5}{2*-4}=\frac{-6}{-8}
=3/4
$