Y=x-4/2x-3

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

=Y-4/2Y-3

We move all terms to the left:

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


Domain of the equation: 2Y-3)!=0

Y∈R


We get rid of parentheses

-Y+4/2Y+3=0

We multiply all the terms by the denominator


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

Wy multiply elements

-2Y^2+6Y+4=0

a = -2; b = 6; c = +4;
Δ = b2-4ac
Δ = 62-4·(-2)·4
Δ = 68
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:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{17}}{2*-2}=\frac{-6-2\sqrt{17}}{-4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{17}}{2*-2}=\frac{-6+2\sqrt{17}}{-4}
$