9x2+4x-17=0

Solution for 9x2+4x-17=0 equation:

9x^2+4x-17=0

a = 9; b = 4; c = -17;
Δ = b2-4ac
Δ = 42-4·9·(-17)
Δ = 628
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:

$\sqrt{\Delta}=\sqrt{628}=\sqrt{4*157}=\sqrt{4}*\sqrt{157}=2\sqrt{157}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{157}}{2*9}=\frac{-4-2\sqrt{157}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{157}}{2*9}=\frac{-4+2\sqrt{157}}{18}
$