(2w+7)w=35

Solution for (2w+7)w=35 equation:

(2w+7)w=35

We move all terms to the left:

(2w+7)w-(35)=0

We multiply parentheses

2w^2+7w-35=0

a = 2; b = 7; c = -35;
Δ = b2-4ac
Δ = 72-4·2·(-35)
Δ = 329
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{329}}{2*2}=\frac{-7-\sqrt{329}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{329}}{2*2}=\frac{-7+\sqrt{329}}{4}
$