10X(x-1)+100=160

Solution for 10X(x-1)+100=160 equation:

10X(X-1)+100=160

We move all terms to the left:

10X(X-1)+100-(160)=0

We add all the numbers together, and all the variables

10X(X-1)-60=0

We multiply parentheses

10X^2-10X-60=0

a = 10; b = -10; c = -60;
Δ = b2-4ac
Δ = -102-4·10·(-60)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-50}{2*10}=\frac{-40}{20}
=-2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+50}{2*10}=\frac{60}{20}
=3
$