2x^2-24x+45=0

Solution for 2x^2-24x+45=0 equation:

2x^2-24x+45=0

a = 2; b = -24; c = +45;
Δ = b2-4ac
Δ = -242-4·2·45
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-6\sqrt{6}}{2*2}=\frac{24-6\sqrt{6}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+6\sqrt{6}}{2*2}=\frac{24+6\sqrt{6}}{4}
$