-56y2/3+58y-40=-5/3

Solution for -56y2/3+58y-40=-5/3 equation:

-56y^2/3+58y-40=-5/3

We move all terms to the left:

-56y^2/3+58y-40-(-5/3)=0

We get rid of parentheses

-56y^2/3+58y-40+5/3=0

We multiply all the terms by the denominator


-56y^2+58y*3+5-40*3=0

We add all the numbers together, and all the variables

-56y^2+58y*3-115=0

Wy multiply elements

-56y^2+174y-115=0

a = -56; b = 174; c = -115;
Δ = b2-4ac
Δ = 1742-4·(-56)·(-115)
Δ = 4516
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:

$\sqrt{\Delta}=\sqrt{4516}=\sqrt{4*1129}=\sqrt{4}*\sqrt{1129}=2\sqrt{1129}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(174)-2\sqrt{1129}}{2*-56}=\frac{-174-2\sqrt{1129}}{-112}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(174)+2\sqrt{1129}}{2*-56}=\frac{-174+2\sqrt{1129}}{-112}
$