Y=3x-9/5x+4

Solution for Y=3x-9/5x+4 equation:

=3Y-9/5Y+4

We move all terms to the left:

-(3Y-9/5Y+4)=0


Domain of the equation: 5Y+4)!=0

Y∈R


We get rid of parentheses

-3Y+9/5Y-4=0

We multiply all the terms by the denominator


-3Y*5Y-4*5Y+9=0

Wy multiply elements

-15Y^2-20Y+9=0

a = -15; b = -20; c = +9;
Δ = b2-4ac
Δ = -202-4·(-15)·9
Δ = 940
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:

$\sqrt{\Delta}=\sqrt{940}=\sqrt{4*235}=\sqrt{4}*\sqrt{235}=2\sqrt{235}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{235}}{2*-15}=\frac{20-2\sqrt{235}}{-30}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{235}}{2*-15}=\frac{20+2\sqrt{235}}{-30}
$