-x^2+13x+30=2x^2

Solution for -x^2+13x+30=2x^2 equation:

-x^2+13x+30=2x^2

We move all terms to the left:

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

determiningTheFunctionDomain
-x^2-2x^2+13x+30=0

We add all the numbers together, and all the variables

-3x^2+13x+30=0

a = -3; b = 13; c = +30;
Δ = b2-4ac
Δ = 132-4·(-3)·30
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-23}{2*-3}=\frac{-36}{-6}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+23}{2*-3}=\frac{10}{-6}
=-1+2/3
$