s(12s+5)=7

Solution for s(12s+5)=7 equation:

s(12s+5)=7

We move all terms to the left:

s(12s+5)-(7)=0

We multiply parentheses

12s^2+5s-7=0

a = 12; b = 5; c = -7;
Δ = b2-4ac
Δ = 52-4·12·(-7)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-19}{2*12}=\frac{-24}{24}
=-1
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+19}{2*12}=\frac{14}{24}
=7/12
$