32x^2-76x+27=0

Solution for 32x^2-76x+27=0 equation:

32x^2-76x+27=0

a = 32; b = -76; c = +27;
Δ = b2-4ac
Δ = -762-4·32·27
Δ = 2320
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:

$\sqrt{\Delta}=\sqrt{2320}=\sqrt{16*145}=\sqrt{16}*\sqrt{145}=4\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-4\sqrt{145}}{2*32}=\frac{76-4\sqrt{145}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+4\sqrt{145}}{2*32}=\frac{76+4\sqrt{145}}{64}
$