S(x)=7/8x+2

Solution for S(x)=7/8x+2 equation:

(S)=7/8S+2

We move all terms to the left:

(S)-(7/8S+2)=0


Domain of the equation: 8S+2)!=0

S∈R


We get rid of parentheses

S-7/8S-2=0

We multiply all the terms by the denominator


S*8S-2*8S-7=0

Wy multiply elements

8S^2-16S-7=0

a = 8; b = -16; c = -7;
Δ = b2-4ac
Δ = -162-4·8·(-7)
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{30}}{2*8}=\frac{16-4\sqrt{30}}{16}
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{30}}{2*8}=\frac{16+4\sqrt{30}}{16}
$