4x^2+17x-32=0

Solution for 4x^2+17x-32=0 equation:

4x^2+17x-32=0

a = 4; b = 17; c = -32;
Δ = b2-4ac
Δ = 172-4·4·(-32)
Δ = 801
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:

$\sqrt{\Delta}=\sqrt{801}=\sqrt{9*89}=\sqrt{9}*\sqrt{89}=3\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-3\sqrt{89}}{2*4}=\frac{-17-3\sqrt{89}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+3\sqrt{89}}{2*4}=\frac{-17+3\sqrt{89}}{8}
$