4g+3g(-7+5g)=1-g

Solution for 4g+3g(-7+5g)=1-g equation:

4g+3g(-7+5g)=1-g

We move all terms to the left:

4g+3g(-7+5g)-(1-g)=0

We add all the numbers together, and all the variables

4g+3g(5g-7)-(-1g+1)=0

We multiply parentheses

15g^2+4g-21g-(-1g+1)=0

We get rid of parentheses

15g^2+4g-21g+1g-1=0

We add all the numbers together, and all the variables

15g^2-16g-1=0

a = 15; b = -16; c = -1;
Δ = b2-4ac
Δ = -162-4·15·(-1)
Δ = 316
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:

$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{79}}{2*15}=\frac{16-2\sqrt{79}}{30}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{79}}{2*15}=\frac{16+2\sqrt{79}}{30}
$