45=x(2x-2)

Solution for 45=x(2x-2) equation:

45=x(2x-2)

We move all terms to the left:

45-(x(2x-2))=0


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

x(2x-2)

We multiply parentheses

2x^2-2x

Back to the equation:

-(2x^2-2x)


We get rid of parentheses

-2x^2+2x+45=0

a = -2; b = 2; c = +45;
Δ = b2-4ac
Δ = 22-4·(-2)·45
Δ = 364
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:

$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{91}}{2*-2}=\frac{-2-2\sqrt{91}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{91}}{2*-2}=\frac{-2+2\sqrt{91}}{-4}
$