-s+5/4s+5=13

Solution for -s+5/4s+5=13 equation:

-s+5/4s+5=13

We move all terms to the left:

-s+5/4s+5-(13)=0


Domain of the equation: 4s!=0

s!=0/4

s!=0

s∈R


We add all the numbers together, and all the variables

-1s+5/4s-8=0

We multiply all the terms by the denominator


-1s*4s-8*4s+5=0

Wy multiply elements

-4s^2-32s+5=0

a = -4; b = -32; c = +5;
Δ = b2-4ac
Δ = -322-4·(-4)·5
Δ = 1104
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:

$\sqrt{\Delta}=\sqrt{1104}=\sqrt{16*69}=\sqrt{16}*\sqrt{69}=4\sqrt{69}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{69}}{2*-4}=\frac{32-4\sqrt{69}}{-8}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{69}}{2*-4}=\frac{32+4\sqrt{69}}{-8}
$