4x+(1/2x)+4=25

Solution for 4x+(1/2x)+4=25 equation:

4x+(1/2x)+4=25

We move all terms to the left:

4x+(1/2x)+4-(25)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4x+(+1/2x)+4-25=0

We add all the numbers together, and all the variables

4x+(+1/2x)-21=0

We get rid of parentheses

4x+1/2x-21=0

We multiply all the terms by the denominator


4x*2x-21*2x+1=0

Wy multiply elements

8x^2-42x+1=0

a = 8; b = -42; c = +1;
Δ = b2-4ac
Δ = -422-4·8·1
Δ = 1732
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1732}=\sqrt{4*433}=\sqrt{4}*\sqrt{433}=2\sqrt{433}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{433}}{2*8}=\frac{42-2\sqrt{433}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{433}}{2*8}=\frac{42+2\sqrt{433}}{16}
$