4x-5=1/25x+32

Solution for 4x-5=1/25x+32 equation:

4x-5=1/25x+32

We move all terms to the left:

4x-5-(1/25x+32)=0


Domain of the equation: 25x+32)!=0

x∈R


We get rid of parentheses

4x-1/25x-32-5=0

We multiply all the terms by the denominator


4x*25x-32*25x-5*25x-1=0

Wy multiply elements

100x^2-800x-125x-1=0

We add all the numbers together, and all the variables

100x^2-925x-1=0

a = 100; b = -925; c = -1;
Δ = b2-4ac
Δ = -9252-4·100·(-1)
Δ = 856025
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:

$\sqrt{\Delta}=\sqrt{856025}=\sqrt{25*34241}=\sqrt{25}*\sqrt{34241}=5\sqrt{34241}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-925)-5\sqrt{34241}}{2*100}=\frac{925-5\sqrt{34241}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-925)+5\sqrt{34241}}{2*100}=\frac{925+5\sqrt{34241}}{200}
$