61=(2w+5)w

Solution for 61=(2w+5)w equation:

61=(2w+5)w

We move all terms to the left:

61-((2w+5)w)=0


We calculate terms in parentheses: -((2w+5)w), so:

(2w+5)w

We multiply parentheses

2w^2+5w

Back to the equation:

-(2w^2+5w)


We get rid of parentheses

-2w^2-5w+61=0

a = -2; b = -5; c = +61;
Δ = b2-4ac
Δ = -52-4·(-2)·61
Δ = 513
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{513}=\sqrt{9*57}=\sqrt{9}*\sqrt{57}=3\sqrt{57}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3\sqrt{57}}{2*-2}=\frac{5-3\sqrt{57}}{-4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3\sqrt{57}}{2*-2}=\frac{5+3\sqrt{57}}{-4}
$