x^2-6x=-15/6

Solution for x^2-6x=-15/6 equation:

x^2-6x=-15/6

We move all terms to the left:

x^2-6x-(-15/6)=0

We get rid of parentheses

x^2-6x+15/6=0

We multiply all the terms by the denominator


x^2*6-6x*6+15=0

Wy multiply elements

6x^2-36x+15=0

a = 6; b = -36; c = +15;
Δ = b2-4ac
Δ = -362-4·6·15
Δ = 936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{936}=\sqrt{36*26}=\sqrt{36}*\sqrt{26}=6\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-6\sqrt{26}}{2*6}=\frac{36-6\sqrt{26}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+6\sqrt{26}}{2*6}=\frac{36+6\sqrt{26}}{12}
$