6w(w+5)=1

Solution for 6w(w+5)=1 equation:

6w(w+5)=1

We move all terms to the left:

6w(w+5)-(1)=0

We multiply parentheses

6w^2+30w-1=0

a = 6; b = 30; c = -1;
Δ = b2-4ac
Δ = 302-4·6·(-1)
Δ = 924
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:

$\sqrt{\Delta}=\sqrt{924}=\sqrt{4*231}=\sqrt{4}*\sqrt{231}=2\sqrt{231}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{231}}{2*6}=\frac{-30-2\sqrt{231}}{12}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{231}}{2*6}=\frac{-30+2\sqrt{231}}{12}
$