4w^2-3w=17

Solution for 4w^2-3w=17 equation:

4w^2-3w=17

We move all terms to the left:

4w^2-3w-(17)=0

a = 4; b = -3; c = -17;
Δ = b2-4ac
Δ = -32-4·4·(-17)
Δ = 281
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{-(-3)-\sqrt{281}}{2*4}=\frac{3-\sqrt{281}}{8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{281}}{2*4}=\frac{3+\sqrt{281}}{8}
$