Y=4x-1/2x-5

Solution for Y=4x-1/2x-5 equation:

=4Y-1/2Y-5

We move all terms to the left:

-(4Y-1/2Y-5)=0


Domain of the equation: 2Y-5)!=0

Y∈R


We get rid of parentheses

-4Y+1/2Y+5=0

We multiply all the terms by the denominator


-4Y*2Y+5*2Y+1=0

Wy multiply elements

-8Y^2+10Y+1=0

a = -8; b = 10; c = +1;
Δ = b2-4ac
Δ = 102-4·(-8)·1
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{33}}{2*-8}=\frac{-10-2\sqrt{33}}{-16}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{33}}{2*-8}=\frac{-10+2\sqrt{33}}{-16}
$