x^2=13.5x

Solution for x^2=13.5x equation:

x^2=13.5x

We move all terms to the left:

x^2-(13.5x)=0

We add all the numbers together, and all the variables

x^2-(+13.5x)=0

We get rid of parentheses

x^2-13.5x=0

a = 1; b = -13.5; c = 0;
Δ = b2-4ac
Δ = -13.52-4·1·0
Δ = 182.25
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{-(-13.5)-\sqrt{182.25}}{2*1}=\frac{13.5-\sqrt{182.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13.5)+\sqrt{182.25}}{2*1}=\frac{13.5+\sqrt{182.25}}{2}
$