2-2s=3/2s+13

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

2-2s=3/2s+13

We move all terms to the left:

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


Domain of the equation: 2s+13)!=0

s∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


-2s*2s-13*2s+2*2s-3=0

Wy multiply elements

-4s^2-26s+4s-3=0

We add all the numbers together, and all the variables

-4s^2-22s-3=0

a = -4; b = -22; c = -3;
Δ = b2-4ac
Δ = -222-4·(-4)·(-3)
Δ = 436
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:

$\sqrt{\Delta}=\sqrt{436}=\sqrt{4*109}=\sqrt{4}*\sqrt{109}=2\sqrt{109}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{109}}{2*-4}=\frac{22-2\sqrt{109}}{-8}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{109}}{2*-4}=\frac{22+2\sqrt{109}}{-8}
$