5w(w+7)=-4w-19

Solution for 5w(w+7)=-4w-19 equation:

5w(w+7)=-4w-19

We move all terms to the left:

5w(w+7)-(-4w-19)=0

We multiply parentheses

5w^2+35w-(-4w-19)=0

We get rid of parentheses

5w^2+35w+4w+19=0

We add all the numbers together, and all the variables

5w^2+39w+19=0

a = 5; b = 39; c = +19;
Δ = b2-4ac
Δ = 392-4·5·19
Δ = 1141
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{-(39)-\sqrt{1141}}{2*5}=\frac{-39-\sqrt{1141}}{10}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+\sqrt{1141}}{2*5}=\frac{-39+\sqrt{1141}}{10}
$