S=5t^2+6t+3t=2

Solution for S=5t^2+6t+3t=2 equation:

=5S^2+6S+3S=2

We move all terms to the left:

-(5S^2+6S+3S)=0

We get rid of parentheses

-5S^2-6S-3S=0

We add all the numbers together, and all the variables

-5S^2-9S=0

a = -5; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·(-5)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*-5}=\frac{0}{-10}
=0
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*-5}=\frac{18}{-10}
=-1+4/5
$