2-2s=3/4s+14

Solution for 2-2s=3/4s+14 equation:

2-2s=3/4s+14

We move all terms to the left:

2-2s-(3/4s+14)=0


Domain of the equation: 4s+14)!=0

s∈R


We get rid of parentheses

-2s-3/4s-14+2=0

We multiply all the terms by the denominator


-2s*4s-14*4s+2*4s-3=0

Wy multiply elements

-8s^2-56s+8s-3=0

We add all the numbers together, and all the variables

-8s^2-48s-3=0

a = -8; b = -48; c = -3;
Δ = b2-4ac
Δ = -482-4·(-8)·(-3)
Δ = 2208
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:

$\sqrt{\Delta}=\sqrt{2208}=\sqrt{16*138}=\sqrt{16}*\sqrt{138}=4\sqrt{138}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{138}}{2*-8}=\frac{48-4\sqrt{138}}{-16}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{138}}{2*-8}=\frac{48+4\sqrt{138}}{-16}
$