2(x^2-5x)=32x

Solution for 2(x^2-5x)=32x equation:

2(x^2-5x)=32x

We move all terms to the left:

2(x^2-5x)-(32x)=0

We add all the numbers together, and all the variables

-32x+2(x^2-5x)=0

We multiply parentheses

2x^2-32x-10x=0

We add all the numbers together, and all the variables

2x^2-42x=0

a = 2; b = -42; c = 0;
Δ = b2-4ac
Δ = -422-4·2·0
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-42}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+42}{2*2}=\frac{84}{4}
=21
$