4*2x=7+1/2x

Solution for 4*2x=7+1/2x equation:

4*2x=7+1/2x

We move all terms to the left:

4*2x-(7+1/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4*2x-(1/2x+7)=0

Wy multiply elements

8x-(1/2x+7)=0

We get rid of parentheses

8x-1/2x-7=0

We multiply all the terms by the denominator


8x*2x-7*2x-1=0

Wy multiply elements

16x^2-14x-1=0

a = 16; b = -14; c = -1;
Δ = b2-4ac
Δ = -142-4·16·(-1)
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{65}}{2*16}=\frac{14-2\sqrt{65}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{65}}{2*16}=\frac{14+2\sqrt{65}}{32}
$