0.75s-5/8s=44

Solution for 0.75s-5/8s=44 equation:

0.75s-5/8s=44

We move all terms to the left:

0.75s-5/8s-(44)=0


Domain of the equation: 8s!=0

s!=0/8

s!=0

s∈R


We multiply all the terms by the denominator


(0.75s)*8s-44*8s-5=0

We add all the numbers together, and all the variables

(+0.75s)*8s-44*8s-5=0

We multiply parentheses

0s^2-44*8s-5=0

Wy multiply elements

0s^2-352s-5=0

We add all the numbers together, and all the variables

s^2-352s-5=0

a = 1; b = -352; c = -5;
Δ = b2-4ac
Δ = -3522-4·1·(-5)
Δ = 123924
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:

$\sqrt{\Delta}=\sqrt{123924}=\sqrt{4*30981}=\sqrt{4}*\sqrt{30981}=2\sqrt{30981}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-352)-2\sqrt{30981}}{2*1}=\frac{352-2\sqrt{30981}}{2}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-352)+2\sqrt{30981}}{2*1}=\frac{352+2\sqrt{30981}}{2}
$