15x=12-x^2

Solution for 15x=12-x^2 equation:

15x=12-x^2

We move all terms to the left:

15x-(12-x^2)=0

We get rid of parentheses

x^2+15x-12=0

a = 1; b = 15; c = -12;
Δ = b2-4ac
Δ = 152-4·1·(-12)
Δ = 273
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{-(15)-\sqrt{273}}{2*1}=\frac{-15-\sqrt{273}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{273}}{2*1}=\frac{-15+\sqrt{273}}{2}
$