g+2g=1/4(2g)+150

Solution for g+2g=1/4(2g)+150 equation:

g+2g=1/4(2g)+150

We move all terms to the left:

g+2g-(1/4(2g)+150)=0


Domain of the equation: 42g+150)!=0

g∈R


We add all the numbers together, and all the variables

3g-(1/42g+150)=0

We get rid of parentheses

3g-1/42g-150=0

We multiply all the terms by the denominator


3g*42g-150*42g-1=0

Wy multiply elements

126g^2-6300g-1=0

a = 126; b = -6300; c = -1;
Δ = b2-4ac
Δ = -63002-4·126·(-1)
Δ = 39690504
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:

$\sqrt{\Delta}=\sqrt{39690504}=\sqrt{36*1102514}=\sqrt{36}*\sqrt{1102514}=6\sqrt{1102514}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6300)-6\sqrt{1102514}}{2*126}=\frac{6300-6\sqrt{1102514}}{252}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6300)+6\sqrt{1102514}}{2*126}=\frac{6300+6\sqrt{1102514}}{252}
$