2-2s=3s/4s+13

Solution for 2-2s=3s/4s+13 equation:

2-2s=3s/4s+13

We move all terms to the left:

2-2s-(3s/4s+13)=0


Domain of the equation: 4s+13)!=0

s∈R


We get rid of parentheses

-2s-3s/4s-13+2=0

We multiply all the terms by the denominator


-2s*4s-3s-13*4s+2*4s=0

We add all the numbers together, and all the variables

-3s-2s*4s-13*4s+2*4s=0

Wy multiply elements

-8s^2-3s-52s+8s=0

We add all the numbers together, and all the variables

-8s^2-47s=0

a = -8; b = -47; c = 0;
Δ = b2-4ac
Δ = -472-4·(-8)·0
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-47}{2*-8}=\frac{0}{-16}
=0
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+47}{2*-8}=\frac{94}{-16}
=-5+7/8
$