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

Solution for 2-1/3s=3/4s+13 equation:

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

We move all terms to the left:

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


Domain of the equation: 3s!=0

s!=0/3

s!=0

s∈R



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

s∈R


We get rid of parentheses

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

We calculate fractions


(-4s)/12s^2+(-9s)/12s^2-13+2=0

We add all the numbers together, and all the variables

(-4s)/12s^2+(-9s)/12s^2-11=0

We multiply all the terms by the denominator


(-4s)+(-9s)-11*12s^2=0

Wy multiply elements

-132s^2+(-4s)+(-9s)=0

We get rid of parentheses

-132s^2-4s-9s=0

We add all the numbers together, and all the variables

-132s^2-13s=0

a = -132; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·(-132)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*-132}=\frac{0}{-264}
=0
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*-132}=\frac{26}{-264}
=-13/132
$