s=3/2*s-30

Solution for s=3/2*s-30 equation:

s=3/2s-30

We move all terms to the left:

s-(3/2s-30)=0


Domain of the equation: 2s-30)!=0

s∈R


We get rid of parentheses

s-3/2s+30=0

We multiply all the terms by the denominator


s*2s+30*2s-3=0

Wy multiply elements

2s^2+60s-3=0

a = 2; b = 60; c = -3;
Δ = b2-4ac
Δ = 602-4·2·(-3)
Δ = 3624
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:

$\sqrt{\Delta}=\sqrt{3624}=\sqrt{4*906}=\sqrt{4}*\sqrt{906}=2\sqrt{906}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-2\sqrt{906}}{2*2}=\frac{-60-2\sqrt{906}}{4}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+2\sqrt{906}}{2*2}=\frac{-60+2\sqrt{906}}{4}
$