2-2s=3/4s-13

Solution for 2-2s=3/4s-13 equation:

2-2s=3/4s-13

We move all terms to the left:

2-2s-(3/4s-13)=0


Domain of the equation: 4s-13)!=0

s∈R


We get rid of parentheses

-2s-3/4s+13+2=0

We multiply all the terms by the denominator


-2s*4s+13*4s+2*4s-3=0

Wy multiply elements

-8s^2+52s+8s-3=0

We add all the numbers together, and all the variables

-8s^2+60s-3=0

a = -8; b = 60; c = -3;
Δ = b2-4ac
Δ = 602-4·(-8)·(-3)
Δ = 3504
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:

$\sqrt{\Delta}=\sqrt{3504}=\sqrt{16*219}=\sqrt{16}*\sqrt{219}=4\sqrt{219}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-4\sqrt{219}}{2*-8}=\frac{-60-4\sqrt{219}}{-16}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+4\sqrt{219}}{2*-8}=\frac{-60+4\sqrt{219}}{-16}
$