(x-5)(2x-90)=360

Solution for (x-5)(2x-90)=360 equation:

(x-5)(2x-90)=360

We move all terms to the left:

(x-5)(2x-90)-(360)=0

We multiply parentheses ..

(+2x^2-90x-10x+450)-360=0

We get rid of parentheses

2x^2-90x-10x+450-360=0

We add all the numbers together, and all the variables

2x^2-100x+90=0

a = 2; b = -100; c = +90;
Δ = b2-4ac
Δ = -1002-4·2·90
Δ = 9280
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:

$\sqrt{\Delta}=\sqrt{9280}=\sqrt{64*145}=\sqrt{64}*\sqrt{145}=8\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-8\sqrt{145}}{2*2}=\frac{100-8\sqrt{145}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+8\sqrt{145}}{2*2}=\frac{100+8\sqrt{145}}{4}
$