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

Solution for 2(2x+15-x^2)=0 equation:

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

We multiply parentheses

-2x^2+4x+30=0

a = -2; b = 4; c = +30;
Δ = b2-4ac
Δ = 42-4·(-2)·30
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-16}{2*-2}=\frac{-20}{-4}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+16}{2*-2}=\frac{12}{-4}
=-3
$