10-4g(g-2)+11=1

Solution for 10-4g(g-2)+11=1 equation:

10-4g(g-2)+11=1

We move all terms to the left:

10-4g(g-2)+11-(1)=0

We add all the numbers together, and all the variables

-4g(g-2)+20=0

We multiply parentheses

-4g^2+8g+20=0

a = -4; b = 8; c = +20;
Δ = b2-4ac
Δ = 82-4·(-4)·20
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{6}}{2*-4}=\frac{-8-8\sqrt{6}}{-8}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{6}}{2*-4}=\frac{-8+8\sqrt{6}}{-8}
$