6w^2+19w-15=-4^2

Solution for 6w^2+19w-15=-4^2 equation:

6w^2+19w-15=-4^2

We move all terms to the left:

6w^2+19w-15-(-4^2)=0

We add all the numbers together, and all the variables

6w^2+19w+1=0

a = 6; b = 19; c = +1;
Δ = b2-4ac
Δ = 192-4·6·1
Δ = 337
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{-(19)-\sqrt{337}}{2*6}=\frac{-19-\sqrt{337}}{12}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{337}}{2*6}=\frac{-19+\sqrt{337}}{12}
$