2x^2-24x+67=0

Solution for 2x^2-24x+67=0 equation:

2x^2-24x+67=0

a = 2; b = -24; c = +67;
Δ = b2-4ac
Δ = -242-4·2·67
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{10}}{2*2}=\frac{24-2\sqrt{10}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{10}}{2*2}=\frac{24+2\sqrt{10}}{4}
$