g+1/2g=352

Solution for g+1/2g=352 equation:

g+1/2g=352

We move all terms to the left:

g+1/2g-(352)=0


Domain of the equation: 2g!=0

g!=0/2

g!=0

g∈R


We multiply all the terms by the denominator


g*2g-352*2g+1=0

Wy multiply elements

2g^2-704g+1=0

a = 2; b = -704; c = +1;
Δ = b2-4ac
Δ = -7042-4·2·1
Δ = 495608
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:

$\sqrt{\Delta}=\sqrt{495608}=\sqrt{4*123902}=\sqrt{4}*\sqrt{123902}=2\sqrt{123902}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-704)-2\sqrt{123902}}{2*2}=\frac{704-2\sqrt{123902}}{4}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-704)+2\sqrt{123902}}{2*2}=\frac{704+2\sqrt{123902}}{4}
$