5x*(3x-31)=10x

Solution for 5x*(3x-31)=10x equation:

5x(3x-31)=10x

We move all terms to the left:

5x(3x-31)-(10x)=0

We add all the numbers together, and all the variables

-10x+5x(3x-31)=0

We multiply parentheses

15x^2-10x-155x=0

We add all the numbers together, and all the variables

15x^2-165x=0

a = 15; b = -165; c = 0;
Δ = b2-4ac
Δ = -1652-4·15·0
Δ = 27225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{27225}=165$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-165)-165}{2*15}=\frac{0}{30}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-165)+165}{2*15}=\frac{330}{30}
=11
$