-7+1/2g+6=4g+10-g

Solution for -7+1/2g+6=4g+10-g equation:

-7+1/2g+6=4g+10-g

We move all terms to the left:

-7+1/2g+6-(4g+10-g)=0


Domain of the equation: 2g!=0

g!=0/2

g!=0

g∈R


We add all the numbers together, and all the variables

1/2g-(3g+10)-7+6=0

We add all the numbers together, and all the variables

1/2g-(3g+10)-1=0

We get rid of parentheses

1/2g-3g-10-1=0

We multiply all the terms by the denominator


-3g*2g-10*2g-1*2g+1=0

Wy multiply elements

-6g^2-20g-2g+1=0

We add all the numbers together, and all the variables

-6g^2-22g+1=0

a = -6; b = -22; c = +1;
Δ = b2-4ac
Δ = -222-4·(-6)·1
Δ = 508
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:

$\sqrt{\Delta}=\sqrt{508}=\sqrt{4*127}=\sqrt{4}*\sqrt{127}=2\sqrt{127}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{127}}{2*-6}=\frac{22-2\sqrt{127}}{-12}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{127}}{2*-6}=\frac{22+2\sqrt{127}}{-12}
$