17x^2+22x-37=0

Solution for 17x^2+22x-37=0 equation:

17x^2+22x-37=0

a = 17; b = 22; c = -37;
Δ = b2-4ac
Δ = 222-4·17·(-37)
Δ = 3000
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:

$\sqrt{\Delta}=\sqrt{3000}=\sqrt{100*30}=\sqrt{100}*\sqrt{30}=10\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-10\sqrt{30}}{2*17}=\frac{-22-10\sqrt{30}}{34}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+10\sqrt{30}}{2*17}=\frac{-22+10\sqrt{30}}{34}
$