(2w-9)(w)=10

Solution for (2w-9)(w)=10 equation:

(2w-9)(w)=10

We move all terms to the left:

(2w-9)(w)-(10)=0

We multiply parentheses

2w^2-9w-10=0

a = 2; b = -9; c = -10;
Δ = b2-4ac
Δ = -92-4·2·(-10)
Δ = 161
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{-(-9)-\sqrt{161}}{2*2}=\frac{9-\sqrt{161}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{161}}{2*2}=\frac{9+\sqrt{161}}{4}
$