Y=1/2x-4x=24

Solution for Y=1/2x-4x=24 equation:

=1/2Y-4Y=24

We move all terms to the left:

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


Domain of the equation: 2Y-4Y)!=0

Y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

4Y-1/2Y=0

We multiply all the terms by the denominator


4Y*2Y-1=0

Wy multiply elements

8Y^2-1=0

a = 8; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·8·(-1)
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{2}}{2*8}=\frac{0-4\sqrt{2}}{16}
=-\frac{4\sqrt{2}}{16}
=-\frac{\sqrt{2}}{4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{2}}{2*8}=\frac{0+4\sqrt{2}}{16}
=\frac{4\sqrt{2}}{16}
=\frac{\sqrt{2}}{4}
$