x^2-10x=5x

Solution for x^2-10x=5x equation:

x^2-10x=5x

We move all terms to the left:

x^2-10x-(5x)=0

We add all the numbers together, and all the variables

x^2-15x=0

a = 1; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·1·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*1}=\frac{0}{2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*1}=\frac{30}{2}
=15
$