2g(g+4)=10+g

Solution for 2g(g+4)=10+g equation:

2g(g+4)=10+g

We move all terms to the left:

2g(g+4)-(10+g)=0

We add all the numbers together, and all the variables

2g(g+4)-(g+10)=0

We multiply parentheses

2g^2+8g-(g+10)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

2g^2+7g-10=0

a = 2; b = 7; c = -10;
Δ = b2-4ac
Δ = 72-4·2·(-10)
Δ = 129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{129}}{2*2}=\frac{-7-\sqrt{129}}{4}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{129}}{2*2}=\frac{-7+\sqrt{129}}{4}
$