17x^2+180x-675=0

Solution for 17x^2+180x-675=0 equation:

17x^2+180x-675=0

a = 17; b = 180; c = -675;
Δ = b2-4ac
Δ = 1802-4·17·(-675)
Δ = 78300
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:

$\sqrt{\Delta}=\sqrt{78300}=\sqrt{900*87}=\sqrt{900}*\sqrt{87}=30\sqrt{87}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-30\sqrt{87}}{2*17}=\frac{-180-30\sqrt{87}}{34}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+30\sqrt{87}}{2*17}=\frac{-180+30\sqrt{87}}{34}
$