114=(2w-7)w

Solution for 114=(2w-7)w equation:

114=(2w-7)w

We move all terms to the left:

114-((2w-7)w)=0


We calculate terms in parentheses: -((2w-7)w), so:

(2w-7)w

We multiply parentheses

2w^2-7w

Back to the equation:

-(2w^2-7w)


We get rid of parentheses

-2w^2+7w+114=0

a = -2; b = 7; c = +114;
Δ = b2-4ac
Δ = 72-4·(-2)·114
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-31}{2*-2}=\frac{-38}{-4}
=9+1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+31}{2*-2}=\frac{24}{-4}
=-6
$