4y^2-22y-84=0

Solution for 4y^2-22y-84=0 equation:

4y^2-22y-84=0

a = 4; b = -22; c = -84;
Δ = b2-4ac
Δ = -222-4·4·(-84)
Δ = 1828
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1828}=\sqrt{4*457}=\sqrt{4}*\sqrt{457}=2\sqrt{457}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{457}}{2*4}=\frac{22-2\sqrt{457}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{457}}{2*4}=\frac{22+2\sqrt{457}}{8}
$