2-2s=3/4s+23

Solution for 2-2s=3/4s+23 equation:

2-2s=3/4s+23

We move all terms to the left:

2-2s-(3/4s+23)=0


Domain of the equation: 4s+23)!=0

s∈R


We get rid of parentheses

-2s-3/4s-23+2=0

We multiply all the terms by the denominator


-2s*4s-23*4s+2*4s-3=0

Wy multiply elements

-8s^2-92s+8s-3=0

We add all the numbers together, and all the variables

-8s^2-84s-3=0

a = -8; b = -84; c = -3;
Δ = b2-4ac
Δ = -842-4·(-8)·(-3)
Δ = 6960
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6960}=\sqrt{16*435}=\sqrt{16}*\sqrt{435}=4\sqrt{435}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-4\sqrt{435}}{2*-8}=\frac{84-4\sqrt{435}}{-16}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+4\sqrt{435}}{2*-8}=\frac{84+4\sqrt{435}}{-16}
$