X2+5x-37=0

Solution for X2+5x-37=0 equation:

X2+5X-37=0

We add all the numbers together, and all the variables

X^2+5X-37=0

a = 1; b = 5; c = -37;
Δ = b2-4ac
Δ = 52-4·1·(-37)
Δ = 173
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{173}}{2*1}=\frac{-5-\sqrt{173}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{173}}{2*1}=\frac{-5+\sqrt{173}}{2}
$