42-64y+24y^2=0

Solution for 42-64y+24y^2=0 equation:

42-64y+24y^2=0

a = 24; b = -64; c = +42;
Δ = b2-4ac
Δ = -642-4·24·42
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-8}{2*24}=\frac{56}{48}
=1+1/6
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+8}{2*24}=\frac{72}{48}
=1+1/2
$