X^2-15x-270=-2x^2+12x

Solution for X^2-15x-270=-2x^2+12x equation:

X^2-15X-270=-2X^2+12X

We move all terms to the left:

X^2-15X-270-(-2X^2+12X)=0

We get rid of parentheses

X^2+2X^2-12X-15X-270=0

We add all the numbers together, and all the variables

3X^2-27X-270=0

a = 3; b = -27; c = -270;
Δ = b2-4ac
Δ = -272-4·3·(-270)
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-63}{2*3}=\frac{-36}{6}
=-6
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+63}{2*3}=\frac{90}{6}
=15
$