365+g(464+76+g)=234

Solution for 365+g(464+76+g)=234 equation:

365+g(464+76+g)=234

We move all terms to the left:

365+g(464+76+g)-(234)=0

We add all the numbers together, and all the variables

g(g+540)+365-234=0

We add all the numbers together, and all the variables

g(g+540)+131=0

We multiply parentheses

g^2+540g+131=0

a = 1; b = 540; c = +131;
Δ = b2-4ac
Δ = 5402-4·1·131
Δ = 291076
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:

$\sqrt{\Delta}=\sqrt{291076}=\sqrt{4*72769}=\sqrt{4}*\sqrt{72769}=2\sqrt{72769}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(540)-2\sqrt{72769}}{2*1}=\frac{-540-2\sqrt{72769}}{2}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(540)+2\sqrt{72769}}{2*1}=\frac{-540+2\sqrt{72769}}{2}
$