2x^2-24x+27=0

Solution for 2x^2-24x+27=0 equation:

2x^2-24x+27=0

a = 2; b = -24; c = +27;
Δ = b2-4ac
Δ = -242-4·2·27
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-6\sqrt{10}}{2*2}=\frac{24-6\sqrt{10}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+6\sqrt{10}}{2*2}=\frac{24+6\sqrt{10}}{4}
$