9+3/2s-8=2s-23

Solution for 9+3/2s-8=2s-23 equation:

9+3/2s-8=2s-23

We move all terms to the left:

9+3/2s-8-(2s-23)=0


Domain of the equation: 2s!=0

s!=0/2

s!=0

s∈R


We add all the numbers together, and all the variables

3/2s-(2s-23)+1=0

We get rid of parentheses

3/2s-2s+23+1=0

We multiply all the terms by the denominator


-2s*2s+23*2s+1*2s+3=0

Wy multiply elements

-4s^2+46s+2s+3=0

We add all the numbers together, and all the variables

-4s^2+48s+3=0

a = -4; b = 48; c = +3;
Δ = b2-4ac
Δ = 482-4·(-4)·3
Δ = 2352
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:

$\sqrt{\Delta}=\sqrt{2352}=\sqrt{784*3}=\sqrt{784}*\sqrt{3}=28\sqrt{3}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-28\sqrt{3}}{2*-4}=\frac{-48-28\sqrt{3}}{-8}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+28\sqrt{3}}{2*-4}=\frac{-48+28\sqrt{3}}{-8}
$