4x^2-6x-32=0

Solution for 4x^2-6x-32=0 equation:

4x^2-6x-32=0

a = 4; b = -6; c = -32;
Δ = b2-4ac
Δ = -62-4·4·(-32)
Δ = 548
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:

$\sqrt{\Delta}=\sqrt{548}=\sqrt{4*137}=\sqrt{4}*\sqrt{137}=2\sqrt{137}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{137}}{2*4}=\frac{6-2\sqrt{137}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{137}}{2*4}=\frac{6+2\sqrt{137}}{8}
$