-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-(14)=0


Domain of the equation: 4s)!=0

s!=0/1

s!=0

s∈R


We add all the numbers together, and all the variables

-s+(+5/4s)+5-14=0

We add all the numbers together, and all the variables

-1s+(+5/4s)-9=0

We get rid of parentheses

-1s+5/4s-9=0

We multiply all the terms by the denominator


-1s*4s-9*4s+5=0

Wy multiply elements

-4s^2-36s+5=0

a = -4; b = -36; c = +5;
Δ = b2-4ac
Δ = -362-4·(-4)·5
Δ = 1376
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:

$\sqrt{\Delta}=\sqrt{1376}=\sqrt{16*86}=\sqrt{16}*\sqrt{86}=4\sqrt{86}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{86}}{2*-4}=\frac{36-4\sqrt{86}}{-8}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{86}}{2*-4}=\frac{36+4\sqrt{86}}{-8}
$