S(d)=7/4d+11

Solution for S(d)=7/4d+11 equation:

(S)=7/4S+11

We move all terms to the left:

(S)-(7/4S+11)=0


Domain of the equation: 4S+11)!=0

S∈R


We get rid of parentheses

S-7/4S-11=0

We multiply all the terms by the denominator


S*4S-11*4S-7=0

Wy multiply elements

4S^2-44S-7=0

a = 4; b = -44; c = -7;
Δ = b2-4ac
Δ = -442-4·4·(-7)
Δ = 2048
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:

$\sqrt{\Delta}=\sqrt{2048}=\sqrt{1024*2}=\sqrt{1024}*\sqrt{2}=32\sqrt{2}$
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-32\sqrt{2}}{2*4}=\frac{44-32\sqrt{2}}{8}
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+32\sqrt{2}}{2*4}=\frac{44+32\sqrt{2}}{8}
$