X2+17x-290=0

Solution for X2+17x-290=0 equation:

X2+17X-290=0

We add all the numbers together, and all the variables

X^2+17X-290=0

a = 1; b = 17; c = -290;
Δ = b2-4ac
Δ = 172-4·1·(-290)
Δ = 1449
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:

$\sqrt{\Delta}=\sqrt{1449}=\sqrt{9*161}=\sqrt{9}*\sqrt{161}=3\sqrt{161}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-3\sqrt{161}}{2*1}=\frac{-17-3\sqrt{161}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+3\sqrt{161}}{2*1}=\frac{-17+3\sqrt{161}}{2}
$