-x^2+15x=49.5

Solution for -x^2+15x=49.5 equation:

-x^2+15x=49.5

We move all terms to the left:

-x^2+15x-(49.5)=0

We add all the numbers together, and all the variables

-1x^2+15x-49.5=0

a = -1; b = 15; c = -49.5;
Δ = b2-4ac
Δ = 152-4·(-1)·(-49.5)
Δ = 27
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{27}=\sqrt{9*3}=\sqrt{9}*\sqrt{3}=3\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{3}}{2*-1}=\frac{-15-3\sqrt{3}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{3}}{2*-1}=\frac{-15+3\sqrt{3}}{-2}
$