X2+18x-65=0

Solution for X2+18x-65=0 equation:

X2+18X-65=0

We add all the numbers together, and all the variables

X^2+18X-65=0

a = 1; b = 18; c = -65;
Δ = b2-4ac
Δ = 182-4·1·(-65)
Δ = 584
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:

$\sqrt{\Delta}=\sqrt{584}=\sqrt{4*146}=\sqrt{4}*\sqrt{146}=2\sqrt{146}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{146}}{2*1}=\frac{-18-2\sqrt{146}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{146}}{2*1}=\frac{-18+2\sqrt{146}}{2}
$