Y=2x+1/4x-3

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

=2Y+1/4Y-3

We move all terms to the left:

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


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

Y∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-8Y^2+12Y-1=0

a = -8; b = 12; c = -1;
Δ = b2-4ac
Δ = 122-4·(-8)·(-1)
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{-(12)-4\sqrt{7}}{2*-8}=\frac{-12-4\sqrt{7}}{-16}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{7}}{2*-8}=\frac{-12+4\sqrt{7}}{-16}
$