6x^2+13x+30=180

Solution for 6x^2+13x+30=180 equation:

6x^2+13x+30=180

We move all terms to the left:

6x^2+13x+30-(180)=0

We add all the numbers together, and all the variables

6x^2+13x-150=0

a = 6; b = 13; c = -150;
Δ = b2-4ac
Δ = 132-4·6·(-150)
Δ = 3769
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)-\sqrt{3769}}{2*6}=\frac{-13-\sqrt{3769}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{3769}}{2*6}=\frac{-13+\sqrt{3769}}{12}
$