4w^2-7w-8w=3

Solution for 4w^2-7w-8w=3 equation:

4w^2-7w-8w=3

We move all terms to the left:

4w^2-7w-8w-(3)=0

We add all the numbers together, and all the variables

4w^2-15w-3=0

a = 4; b = -15; c = -3;
Δ = b2-4ac
Δ = -152-4·4·(-3)
Δ = 273
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{-(-15)-\sqrt{273}}{2*4}=\frac{15-\sqrt{273}}{8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{273}}{2*4}=\frac{15+\sqrt{273}}{8}
$