2s^2+7s=s^2+2+72

Solution for 2s^2+7s=s^2+2+72 equation:

2s^2+7s=s^2+2+72

We move all terms to the left:

2s^2+7s-(s^2+2+72)=0

We get rid of parentheses

2s^2-s^2+7s-2-72=0

We add all the numbers together, and all the variables

s^2+7s-74=0

a = 1; b = 7; c = -74;
Δ = b2-4ac
Δ = 72-4·1·(-74)
Δ = 345
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{345}}{2*1}=\frac{-7-\sqrt{345}}{2}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{345}}{2*1}=\frac{-7+\sqrt{345}}{2}
$