(2x-1)(x-10)=90

Solution for (2x-1)(x-10)=90 equation:

(2x-1)(x-10)=90

We move all terms to the left:

(2x-1)(x-10)-(90)=0

We multiply parentheses ..

(+2x^2-20x-1x+10)-90=0

We get rid of parentheses

2x^2-20x-1x+10-90=0

We add all the numbers together, and all the variables

2x^2-21x-80=0

a = 2; b = -21; c = -80;
Δ = b2-4ac
Δ = -212-4·2·(-80)
Δ = 1081
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-\sqrt{1081}}{2*2}=\frac{21-\sqrt{1081}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{1081}}{2*2}=\frac{21+\sqrt{1081}}{4}
$