4x2-28x+27=0

Solution for 4x2-28x+27=0 equation:

4x^2-28x+27=0

a = 4; b = -28; c = +27;
Δ = b2-4ac
Δ = -282-4·4·27
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{22}}{2*4}=\frac{28-4\sqrt{22}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{22}}{2*4}=\frac{28+4\sqrt{22}}{8}
$