Y=6x+2/2x-9

Solution for Y=6x+2/2x-9 equation:

=6Y+2/2Y-9

We move all terms to the left:

-(6Y+2/2Y-9)=0


Domain of the equation: 2Y-9)!=0

Y∈R


We get rid of parentheses

-6Y-2/2Y+9=0

We multiply all the terms by the denominator


-6Y*2Y+9*2Y-2=0

Wy multiply elements

-12Y^2+18Y-2=0

a = -12; b = 18; c = -2;
Δ = b2-4ac
Δ = 182-4·(-12)·(-2)
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{57}}{2*-12}=\frac{-18-2\sqrt{57}}{-24}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{57}}{2*-12}=\frac{-18+2\sqrt{57}}{-24}
$