18x-6=5x^2+5x

Solution for 18x-6=5x^2+5x equation:

18x-6=5x^2+5x

We move all terms to the left:

18x-6-(5x^2+5x)=0

We get rid of parentheses

-5x^2+18x-5x-6=0

We add all the numbers together, and all the variables

-5x^2+13x-6=0

a = -5; b = 13; c = -6;
Δ = b2-4ac
Δ = 132-4·(-5)·(-6)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-7}{2*-5}=\frac{-20}{-10}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+7}{2*-5}=\frac{-6}{-10}
=3/5
$