25/5x=64-32x

Solution for 25/5x=64-32x equation:

25/5x=64-32x

We move all terms to the left:

25/5x-(64-32x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

25/5x-(-32x+64)=0

We get rid of parentheses

25/5x+32x-64=0

We multiply all the terms by the denominator


32x*5x-64*5x+25=0

Wy multiply elements

160x^2-320x+25=0

a = 160; b = -320; c = +25;
Δ = b2-4ac
Δ = -3202-4·160·25
Δ = 86400
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:

$\sqrt{\Delta}=\sqrt{86400}=\sqrt{14400*6}=\sqrt{14400}*\sqrt{6}=120\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-320)-120\sqrt{6}}{2*160}=\frac{320-120\sqrt{6}}{320}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-320)+120\sqrt{6}}{2*160}=\frac{320+120\sqrt{6}}{320}
$