X^2+10x-83=0

Solution for X^2+10x-83=0 equation:

X^2+10X-83=0

a = 1; b = 10; c = -83;
Δ = b2-4ac
Δ = 102-4·1·(-83)
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-12\sqrt{3}}{2*1}=\frac{-10-12\sqrt{3}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+12\sqrt{3}}{2*1}=\frac{-10+12\sqrt{3}}{2}
$