-x2+18x-37=0

Solution for -x2+18x-37=0 equation:

-x2+18x-37=0

We add all the numbers together, and all the variables

-1x^2+18x-37=0

a = -1; b = 18; c = -37;
Δ = b2-4ac
Δ = 182-4·(-1)·(-37)
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-4\sqrt{11}}{2*-1}=\frac{-18-4\sqrt{11}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+4\sqrt{11}}{2*-1}=\frac{-18+4\sqrt{11}}{-2}
$