6-2x2=9x+15

Solution for 6-2x2=9x+15 equation:

6-2x^2=9x+15

We move all terms to the left:

6-2x^2-(9x+15)=0

We get rid of parentheses

-2x^2-9x-15+6=0

We add all the numbers together, and all the variables

-2x^2-9x-9=0

a = -2; b = -9; c = -9;
Δ = b2-4ac
Δ = -92-4·(-2)·(-9)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3}{2*-2}=\frac{6}{-4}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3}{2*-2}=\frac{12}{-4}
=-3
$