-x^2+30x-175=0

Solution for -x^2+30x-175=0 equation:

-x^2+30x-175=0

We add all the numbers together, and all the variables

-1x^2+30x-175=0

a = -1; b = 30; c = -175;
Δ = b2-4ac
Δ = 302-4·(-1)·(-175)
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-10\sqrt{2}}{2*-1}=\frac{-30-10\sqrt{2}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+10\sqrt{2}}{2*-1}=\frac{-30+10\sqrt{2}}{-2}
$