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

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

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

We move all terms to the left:

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


Domain of the equation: 4s!=0

s!=0/4

s!=0

s∈R



Domain of the equation: 3s+4)!=0

s∈R


We get rid of parentheses

-3/4s-1/3s-4-3=0

We calculate fractions


(-9s)/12s^2+(-4s)/12s^2-4-3=0

We add all the numbers together, and all the variables

(-9s)/12s^2+(-4s)/12s^2-7=0

We multiply all the terms by the denominator


(-9s)+(-4s)-7*12s^2=0

Wy multiply elements

-84s^2+(-9s)+(-4s)=0

We get rid of parentheses

-84s^2-9s-4s=0

We add all the numbers together, and all the variables

-84s^2-13s=0

a = -84; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·(-84)·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*-84}=\frac{0}{-168}
=0
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*-84}=\frac{26}{-168}
=-13/84
$