-5x2+32x-6=0

Solution for -5x2+32x-6=0 equation:

-5x^2+32x-6=0

a = -5; b = 32; c = -6;
Δ = b2-4ac
Δ = 322-4·(-5)·(-6)
Δ = 904
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:

$\sqrt{\Delta}=\sqrt{904}=\sqrt{4*226}=\sqrt{4}*\sqrt{226}=2\sqrt{226}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-2\sqrt{226}}{2*-5}=\frac{-32-2\sqrt{226}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+2\sqrt{226}}{2*-5}=\frac{-32+2\sqrt{226}}{-10}
$