(s+7)(s-7)=48s

Solution for (s+7)(s-7)=48s equation:

(s+7)(s-7)=48s

We move all terms to the left:

(s+7)(s-7)-(48s)=0

We add all the numbers together, and all the variables

-48s+(s+7)(s-7)=0

We use the square of the difference formula

s^2-48s-49=0

a = 1; b = -48; c = -49;
Δ = b2-4ac
Δ = -482-4·1·(-49)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-50}{2*1}=\frac{-2}{2}
=-1
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+50}{2*1}=\frac{98}{2}
=49
$