5-2g=1/2g-4

Solution for 5-2g=1/2g-4 equation:

5-2g=1/2g-4

We move all terms to the left:

5-2g-(1/2g-4)=0


Domain of the equation: 2g-4)!=0

g∈R


We get rid of parentheses

-2g-1/2g+4+5=0

We multiply all the terms by the denominator


-2g*2g+4*2g+5*2g-1=0

Wy multiply elements

-4g^2+8g+10g-1=0

We add all the numbers together, and all the variables

-4g^2+18g-1=0

a = -4; b = 18; c = -1;
Δ = b2-4ac
Δ = 182-4·(-4)·(-1)
Δ = 308
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:

$\sqrt{\Delta}=\sqrt{308}=\sqrt{4*77}=\sqrt{4}*\sqrt{77}=2\sqrt{77}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{77}}{2*-4}=\frac{-18-2\sqrt{77}}{-8}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{77}}{2*-4}=\frac{-18+2\sqrt{77}}{-8}
$