w^2=-(7w+3)

Solution for w^2=-(7w+3) equation:

w^2=-(7w+3)

We move all terms to the left:

w^2-(-(7w+3))=0


We calculate terms in parentheses: -(-(7w+3)), so:

-(7w+3)

We get rid of parentheses

-7w-3

Back to the equation:

-(-7w-3)


We get rid of parentheses

w^2+7w+3=0

a = 1; b = 7; c = +3;
Δ = b2-4ac
Δ = 72-4·1·3
Δ = 37
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{37}}{2*1}=\frac{-7-\sqrt{37}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{37}}{2*1}=\frac{-7+\sqrt{37}}{2}
$