-x^2+32x-68=0

Solution for -x^2+32x-68=0 equation:

-x^2+32x-68=0

We add all the numbers together, and all the variables

-1x^2+32x-68=0

a = -1; b = 32; c = -68;
Δ = b2-4ac
Δ = 322-4·(-1)·(-68)
Δ = 752
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:

$\sqrt{\Delta}=\sqrt{752}=\sqrt{16*47}=\sqrt{16}*\sqrt{47}=4\sqrt{47}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{47}}{2*-1}=\frac{-32-4\sqrt{47}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{47}}{2*-1}=\frac{-32+4\sqrt{47}}{-2}
$