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

Solution for -2x^2+18x+37=0 equation:

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

a = -2; b = 18; c = +37;
Δ = b2-4ac
Δ = 182-4·(-2)·37
Δ = 620
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:

$\sqrt{\Delta}=\sqrt{620}=\sqrt{4*155}=\sqrt{4}*\sqrt{155}=2\sqrt{155}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{155}}{2*-2}=\frac{-18-2\sqrt{155}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{155}}{2*-2}=\frac{-18+2\sqrt{155}}{-4}
$