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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

10w^2+19w-15=0

a = 10; b = 19; c = -15;
Δ = b2-4ac
Δ = 192-4·10·(-15)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-31}{2*10}=\frac{-50}{20}
=-2+1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+31}{2*10}=\frac{12}{20}
=3/5
$