g^2-34g+240=24

Solution for g^2-34g+240=24 equation:

g^2-34g+240=24

We move all terms to the left:

g^2-34g+240-(24)=0

We add all the numbers together, and all the variables

g^2-34g+216=0

a = 1; b = -34; c = +216;
Δ = b2-4ac
Δ = -342-4·1·216
Δ = 292
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{73}}{2*1}=\frac{34-2\sqrt{73}}{2}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{73}}{2*1}=\frac{34+2\sqrt{73}}{2}
$