1/4s-3=33/10s-7

Solution for 1/4s-3=33/10s-7 equation:

1/4s-3=33/10s-7

We move all terms to the left:

1/4s-3-(33/10s-7)=0


Domain of the equation: 4s!=0

s!=0/4

s!=0

s∈R



Domain of the equation: 10s-7)!=0

s∈R


We get rid of parentheses

1/4s-33/10s+7-3=0

We calculate fractions


10s/40s^2+(-132s)/40s^2+7-3=0

We add all the numbers together, and all the variables

10s/40s^2+(-132s)/40s^2+4=0

We multiply all the terms by the denominator


10s+(-132s)+4*40s^2=0

Wy multiply elements

160s^2+10s+(-132s)=0

We get rid of parentheses

160s^2+10s-132s=0

We add all the numbers together, and all the variables

160s^2-122s=0

a = 160; b = -122; c = 0;
Δ = b2-4ac
Δ = -1222-4·160·0
Δ = 14884
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14884}=122$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-122)-122}{2*160}=\frac{0}{320}
=0
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-122)+122}{2*160}=\frac{244}{320}
=61/80
$