1/2g-5=2g+10

Solution for 1/2g-5=2g+10 equation:

1/2g-5=2g+10

We move all terms to the left:

1/2g-5-(2g+10)=0


Domain of the equation: 2g!=0

g!=0/2

g!=0

g∈R


We get rid of parentheses

1/2g-2g-10-5=0

We multiply all the terms by the denominator


-2g*2g-10*2g-5*2g+1=0

Wy multiply elements

-4g^2-20g-10g+1=0

We add all the numbers together, and all the variables

-4g^2-30g+1=0

a = -4; b = -30; c = +1;
Δ = b2-4ac
Δ = -302-4·(-4)·1
Δ = 916
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:

$\sqrt{\Delta}=\sqrt{916}=\sqrt{4*229}=\sqrt{4}*\sqrt{229}=2\sqrt{229}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{229}}{2*-4}=\frac{30-2\sqrt{229}}{-8}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{229}}{2*-4}=\frac{30+2\sqrt{229}}{-8}
$