5g+4g(-5+3g)=1-g

Solution for 5g+4g(-5+3g)=1-g equation:

5g+4g(-5+3g)=1-g

We move all terms to the left:

5g+4g(-5+3g)-(1-g)=0

We add all the numbers together, and all the variables

5g+4g(3g-5)-(-1g+1)=0

We multiply parentheses

12g^2+5g-20g-(-1g+1)=0

We get rid of parentheses

12g^2+5g-20g+1g-1=0

We add all the numbers together, and all the variables

12g^2-14g-1=0

a = 12; b = -14; c = -1;
Δ = b2-4ac
Δ = -142-4·12·(-1)
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{61}}{2*12}=\frac{14-2\sqrt{61}}{24}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{61}}{2*12}=\frac{14+2\sqrt{61}}{24}
$