7s2=4(s+1)

Solution for 7s2=4(s+1) equation:

7s^2=4(s+1)

We move all terms to the left:

7s^2-(4(s+1))=0


We calculate terms in parentheses: -(4(s+1)), so:

4(s+1)

We multiply parentheses

4s+4

Back to the equation:

-(4s+4)


We get rid of parentheses

7s^2-4s-4=0

a = 7; b = -4; c = -4;
Δ = b2-4ac
Δ = -42-4·7·(-4)
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8\sqrt{2}}{2*7}=\frac{4-8\sqrt{2}}{14}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8\sqrt{2}}{2*7}=\frac{4+8\sqrt{2}}{14}
$