7g+9^2-11g=g(4+11g)

Solution for 7g+9^2-11g=g(4+11g) equation:

7g+9^2-11g=g(4+11g)

We move all terms to the left:

7g+9^2-11g-(g(4+11g))=0

We add all the numbers together, and all the variables

7g-11g-(g(11g+4))+9^2=0

We add all the numbers together, and all the variables

-4g-(g(11g+4))+81=0


We calculate terms in parentheses: -(g(11g+4)), so:

g(11g+4)

We multiply parentheses

11g^2+4g

Back to the equation:

-(11g^2+4g)


We get rid of parentheses

-11g^2-4g-4g+81=0

We add all the numbers together, and all the variables

-11g^2-8g+81=0

a = -11; b = -8; c = +81;
Δ = b2-4ac
Δ = -82-4·(-11)·81
Δ = 3628
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:

$\sqrt{\Delta}=\sqrt{3628}=\sqrt{4*907}=\sqrt{4}*\sqrt{907}=2\sqrt{907}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{907}}{2*-11}=\frac{8-2\sqrt{907}}{-22}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{907}}{2*-11}=\frac{8+2\sqrt{907}}{-22}
$