32(x+3)-5=813/4x

Solution for 32(x+3)-5=813/4x equation:

32(x+3)-5=813/4x

We move all terms to the left:

32(x+3)-5-(813/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

32(x+3)-(+813/4x)-5=0

We multiply parentheses

32x-(+813/4x)+96-5=0

We get rid of parentheses

32x-813/4x+96-5=0

We multiply all the terms by the denominator


32x*4x+96*4x-5*4x-813=0

Wy multiply elements

128x^2+384x-20x-813=0

We add all the numbers together, and all the variables

128x^2+364x-813=0

a = 128; b = 364; c = -813;
Δ = b2-4ac
Δ = 3642-4·128·(-813)
Δ = 548752
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:

$\sqrt{\Delta}=\sqrt{548752}=\sqrt{16*34297}=\sqrt{16}*\sqrt{34297}=4\sqrt{34297}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(364)-4\sqrt{34297}}{2*128}=\frac{-364-4\sqrt{34297}}{256}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(364)+4\sqrt{34297}}{2*128}=\frac{-364+4\sqrt{34297}}{256}
$