2-2s-3/4s=13

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

2-2s-3/4s=13

We move all terms to the left:

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


Domain of the equation: 4s!=0

s!=0/4

s!=0

s∈R


We add all the numbers together, and all the variables

-2s-3/4s-11=0

We multiply all the terms by the denominator


-2s*4s-11*4s-3=0

Wy multiply elements

-8s^2-44s-3=0

a = -8; b = -44; c = -3;
Δ = b2-4ac
Δ = -442-4·(-8)·(-3)
Δ = 1840
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:

$\sqrt{\Delta}=\sqrt{1840}=\sqrt{16*115}=\sqrt{16}*\sqrt{115}=4\sqrt{115}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-4\sqrt{115}}{2*-8}=\frac{44-4\sqrt{115}}{-16}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+4\sqrt{115}}{2*-8}=\frac{44+4\sqrt{115}}{-16}
$