Y=2x-8/3x-4

Solution for Y=2x-8/3x-4 equation:

=2Y-8/3Y-4

We move all terms to the left:

-(2Y-8/3Y-4)=0


Domain of the equation: 3Y-4)!=0

Y∈R


We get rid of parentheses

-2Y+8/3Y+4=0

We multiply all the terms by the denominator


-2Y*3Y+4*3Y+8=0

Wy multiply elements

-6Y^2+12Y+8=0

a = -6; b = 12; c = +8;
Δ = b2-4ac
Δ = 122-4·(-6)·8
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{21}}{2*-6}=\frac{-12-4\sqrt{21}}{-12}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{21}}{2*-6}=\frac{-12+4\sqrt{21}}{-12}
$