S+2(s+3)4s-5=148

Solution for S+2(s+3)4s-5=148 equation:

+2(S+3)4S-5=148

We move all terms to the left:

+2(S+3)4S-5-(148)=0

We add all the numbers together, and all the variables

2(S+3)4S-153=0

We multiply parentheses

8S^2+24S-153=0

a = 8; b = 24; c = -153;
Δ = b2-4ac
Δ = 242-4·8·(-153)
Δ = 5472
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:

$\sqrt{\Delta}=\sqrt{5472}=\sqrt{144*38}=\sqrt{144}*\sqrt{38}=12\sqrt{38}$
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-12\sqrt{38}}{2*8}=\frac{-24-12\sqrt{38}}{16}
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+12\sqrt{38}}{2*8}=\frac{-24+12\sqrt{38}}{16}
$