2-s=3/4s+13

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

2-s=3/4s+13

We move all terms to the left:

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


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

s∈R


We add all the numbers together, and all the variables

-1s-(3/4s+13)+2=0

We get rid of parentheses

-1s-3/4s-13+2=0

We multiply all the terms by the denominator


-1s*4s-13*4s+2*4s-3=0

Wy multiply elements

-4s^2-52s+8s-3=0

We add all the numbers together, and all the variables

-4s^2-44s-3=0

a = -4; b = -44; c = -3;
Δ = b2-4ac
Δ = -442-4·(-4)·(-3)
Δ = 1888
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:

$\sqrt{\Delta}=\sqrt{1888}=\sqrt{16*118}=\sqrt{16}*\sqrt{118}=4\sqrt{118}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-4\sqrt{118}}{2*-4}=\frac{44-4\sqrt{118}}{-8}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+4\sqrt{118}}{2*-4}=\frac{44+4\sqrt{118}}{-8}
$