1350x-67050/5x+40=1

Solution for 1350x-67050/5x+40=1 equation:

1350x-67050/5x+40=1

We move all terms to the left:

1350x-67050/5x+40-(1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

1350x-67050/5x+39=0

We multiply all the terms by the denominator


1350x*5x+39*5x-67050=0

Wy multiply elements

6750x^2+195x-67050=0

a = 6750; b = 195; c = -67050;
Δ = b2-4ac
Δ = 1952-4·6750·(-67050)
Δ = 1810388025
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:

$\sqrt{\Delta}=\sqrt{1810388025}=\sqrt{225*8046169}=\sqrt{225}*\sqrt{8046169}=15\sqrt{8046169}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(195)-15\sqrt{8046169}}{2*6750}=\frac{-195-15\sqrt{8046169}}{13500}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(195)+15\sqrt{8046169}}{2*6750}=\frac{-195+15\sqrt{8046169}}{13500}
$