x+(116/8x)=43.5

Solution for x+(116/8x)=43.5 equation:

x+(116/8x)=43.5

We move all terms to the left:

x+(116/8x)-(43.5)=0


Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x+(+116/8x)-(43.5)=0

We add all the numbers together, and all the variables

x+(+116/8x)-43.5=0

We get rid of parentheses

x+116/8x-43.5=0

We multiply all the terms by the denominator


x*8x-(43.5)*8x+116=0

We multiply parentheses

x*8x-348x+116=0

Wy multiply elements

8x^2-348x+116=0

a = 8; b = -348; c = +116;
Δ = b2-4ac
Δ = -3482-4·8·116
Δ = 117392
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:

$\sqrt{\Delta}=\sqrt{117392}=\sqrt{16*7337}=\sqrt{16}*\sqrt{7337}=4\sqrt{7337}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-348)-4\sqrt{7337}}{2*8}=\frac{348-4\sqrt{7337}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-348)+4\sqrt{7337}}{2*8}=\frac{348+4\sqrt{7337}}{16}
$