Y=5x-2/4x+3

Solution for Y=5x-2/4x+3 equation:

=5Y-2/4Y+3

We move all terms to the left:

-(5Y-2/4Y+3)=0


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

Y∈R


We get rid of parentheses

-5Y+2/4Y-3=0

We multiply all the terms by the denominator


-5Y*4Y-3*4Y+2=0

Wy multiply elements

-20Y^2-12Y+2=0

a = -20; b = -12; c = +2;
Δ = b2-4ac
Δ = -122-4·(-20)·2
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{19}}{2*-20}=\frac{12-4\sqrt{19}}{-40}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{19}}{2*-20}=\frac{12+4\sqrt{19}}{-40}
$