11g-1=-9g(-4g-11)

Solution for 11g-1=-9g(-4g-11) equation:

11g-1=-9g(-4g-11)

We move all terms to the left:

11g-1-(-9g(-4g-11))=0


We calculate terms in parentheses: -(-9g(-4g-11)), so:

-9g(-4g-11)

We multiply parentheses

36g^2+99g

Back to the equation:

-(36g^2+99g)


We get rid of parentheses

-36g^2+11g-99g-1=0

We add all the numbers together, and all the variables

-36g^2-88g-1=0

a = -36; b = -88; c = -1;
Δ = b2-4ac
Δ = -882-4·(-36)·(-1)
Δ = 7600
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:

$\sqrt{\Delta}=\sqrt{7600}=\sqrt{400*19}=\sqrt{400}*\sqrt{19}=20\sqrt{19}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88)-20\sqrt{19}}{2*-36}=\frac{88-20\sqrt{19}}{-72}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88)+20\sqrt{19}}{2*-36}=\frac{88+20\sqrt{19}}{-72}
$