3/4x+5=54x+25

Solution for 3/4x+5=54x+25 equation:

3/4x+5=54x+25

We move all terms to the left:

3/4x+5-(54x+25)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

3/4x-54x-25+5=0

We multiply all the terms by the denominator


-54x*4x-25*4x+5*4x+3=0

Wy multiply elements

-216x^2-100x+20x+3=0

We add all the numbers together, and all the variables

-216x^2-80x+3=0

a = -216; b = -80; c = +3;
Δ = b2-4ac
Δ = -802-4·(-216)·3
Δ = 8992
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:

$\sqrt{\Delta}=\sqrt{8992}=\sqrt{16*562}=\sqrt{16}*\sqrt{562}=4\sqrt{562}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-4\sqrt{562}}{2*-216}=\frac{80-4\sqrt{562}}{-432}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+4\sqrt{562}}{2*-216}=\frac{80+4\sqrt{562}}{-432}
$