Y=15x-30/x-4

Solution for Y=15x-30/x-4 equation:

=15Y-30/Y-4

We move all terms to the left:

-(15Y-30/Y-4)=0


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

Y∈R


We get rid of parentheses

-15Y+30/Y+4=0

We multiply all the terms by the denominator


-15Y*Y+4*Y+30=0

We add all the numbers together, and all the variables

4Y-15Y*Y+30=0

Wy multiply elements

-15Y^2+4Y+30=0

a = -15; b = 4; c = +30;
Δ = b2-4ac
Δ = 42-4·(-15)·30
Δ = 1816
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:

$\sqrt{\Delta}=\sqrt{1816}=\sqrt{4*454}=\sqrt{4}*\sqrt{454}=2\sqrt{454}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{454}}{2*-15}=\frac{-4-2\sqrt{454}}{-30}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{454}}{2*-15}=\frac{-4+2\sqrt{454}}{-30}
$