2x(x-10)+3(x-20)=100

Solution for 2x(x-10)+3(x-20)=100 equation:

2x(x-10)+3(x-20)=100

We move all terms to the left:

2x(x-10)+3(x-20)-(100)=0

We multiply parentheses

2x^2-20x+3x-60-100=0

We add all the numbers together, and all the variables

2x^2-17x-160=0

a = 2; b = -17; c = -160;
Δ = b2-4ac
Δ = -172-4·2·(-160)
Δ = 1569
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{-(-17)-\sqrt{1569}}{2*2}=\frac{17-\sqrt{1569}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{1569}}{2*2}=\frac{17+\sqrt{1569}}{4}
$