Y=2x-3/4x+1

Solution for Y=2x-3/4x+1 equation:

=2Y-3/4Y+1

We move all terms to the left:

-(2Y-3/4Y+1)=0


Domain of the equation: 4Y+1)!=0

Y∈R


We get rid of parentheses

-2Y+3/4Y-1=0

We multiply all the terms by the denominator


-2Y*4Y-1*4Y+3=0

Wy multiply elements

-8Y^2-4Y+3=0

a = -8; b = -4; c = +3;
Δ = b2-4ac
Δ = -42-4·(-8)·3
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{7}}{2*-8}=\frac{4-4\sqrt{7}}{-16}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{7}}{2*-8}=\frac{4+4\sqrt{7}}{-16}
$