-s=5/4s+5=14

Solution for -s=5/4s+5=14 equation:

-s=5/4s+5=14

We move all terms to the left:

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


Domain of the equation: 4s+5)!=0

s∈R


We add all the numbers together, and all the variables

-1s-(5/4s+5)=0

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-4s^2-20s-5=0

a = -4; b = -20; c = -5;
Δ = b2-4ac
Δ = -202-4·(-4)·(-5)
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-8\sqrt{5}}{2*-4}=\frac{20-8\sqrt{5}}{-8}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+8\sqrt{5}}{2*-4}=\frac{20+8\sqrt{5}}{-8}
$