1/2g+7=2g

Solution for 1/2g+7=2g equation:

1/2g+7=2g

We move all terms to the left:

1/2g+7-(2g)=0


Domain of the equation: 2g!=0

g!=0/2

g!=0

g∈R


We add all the numbers together, and all the variables

-2g+1/2g+7=0

We multiply all the terms by the denominator


-2g*2g+7*2g+1=0

Wy multiply elements

-4g^2+14g+1=0

a = -4; b = 14; c = +1;
Δ = b2-4ac
Δ = 142-4·(-4)·1
Δ = 212
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:

$\sqrt{\Delta}=\sqrt{212}=\sqrt{4*53}=\sqrt{4}*\sqrt{53}=2\sqrt{53}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{53}}{2*-4}=\frac{-14-2\sqrt{53}}{-8}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{53}}{2*-4}=\frac{-14+2\sqrt{53}}{-8}
$