-s+5/4s+5=4

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

-s+5/4s+5=4

We move all terms to the left:

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -4; b = 4; c = +5;
Δ = b2-4ac
Δ = 42-4·(-4)·5
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{6}}{2*-4}=\frac{-4-4\sqrt{6}}{-8}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{6}}{2*-4}=\frac{-4+4\sqrt{6}}{-8}
$