17/4-3y^2-7y=0

Solution for 17/4-3y^2-7y=0 equation:

17/4-3y^2-7y=0

We multiply all the terms by the denominator


-3y^2*4-7y*4+17=0

Wy multiply elements

-12y^2-28y+17=0

a = -12; b = -28; c = +17;
Δ = b2-4ac
Δ = -282-4·(-12)·17
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-40}{2*-12}=\frac{-12}{-24}
=1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+40}{2*-12}=\frac{68}{-24}
=-2+5/6
$