(x-5)(2x-18)=0

Solution for (x-5)(2x-18)=0 equation:

(x-5)(2x-18)=0

We multiply parentheses ..

(+2x^2-18x-10x+90)=0

We get rid of parentheses

2x^2-18x-10x+90=0

We add all the numbers together, and all the variables

2x^2-28x+90=0

a = 2; b = -28; c = +90;
Δ = b2-4ac
Δ = -282-4·2·90
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-8}{2*2}=\frac{20}{4}
=5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+8}{2*2}=\frac{36}{4}
=9
$