S(d)=1/2d+30

Solution for S(d)=1/2d+30 equation:

(S)=1/2S+30

We move all terms to the left:

(S)-(1/2S+30)=0


Domain of the equation: 2S+30)!=0

S∈R


We get rid of parentheses

S-1/2S-30=0

We multiply all the terms by the denominator


S*2S-30*2S-1=0

Wy multiply elements

2S^2-60S-1=0

a = 2; b = -60; c = -1;
Δ = b2-4ac
Δ = -602-4·2·(-1)
Δ = 3608
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:

$\sqrt{\Delta}=\sqrt{3608}=\sqrt{4*902}=\sqrt{4}*\sqrt{902}=2\sqrt{902}$
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{902}}{2*2}=\frac{60-2\sqrt{902}}{4}
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{902}}{2*2}=\frac{60+2\sqrt{902}}{4}
$