(10x-2)(x-1)=100

Solution for (10x-2)(x-1)=100 equation:

(10x-2)(x-1)=100

We move all terms to the left:

(10x-2)(x-1)-(100)=0

We multiply parentheses ..

(+10x^2-10x-2x+2)-100=0

We get rid of parentheses

10x^2-10x-2x+2-100=0

We add all the numbers together, and all the variables

10x^2-12x-98=0

a = 10; b = -12; c = -98;
Δ = b2-4ac
Δ = -122-4·10·(-98)
Δ = 4064
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:

$\sqrt{\Delta}=\sqrt{4064}=\sqrt{16*254}=\sqrt{16}*\sqrt{254}=4\sqrt{254}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{254}}{2*10}=\frac{12-4\sqrt{254}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{254}}{2*10}=\frac{12+4\sqrt{254}}{20}
$