-4w^2-7w+6=0

Solution for -4w^2-7w+6=0 equation:

-4w^2-7w+6=0

a = -4; b = -7; c = +6;
Δ = b2-4ac
Δ = -72-4·(-4)·6
Δ = 145
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{-(-7)-\sqrt{145}}{2*-4}=\frac{7-\sqrt{145}}{-8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{145}}{2*-4}=\frac{7+\sqrt{145}}{-8}
$