4x+2/5x-6=1

Solution for 4x+2/5x-6=1 equation:

4x+2/5x-6=1

We move all terms to the left:

4x+2/5x-6-(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

4x+2/5x-7=0

We multiply all the terms by the denominator


4x*5x-7*5x+2=0

Wy multiply elements

20x^2-35x+2=0

a = 20; b = -35; c = +2;
Δ = b2-4ac
Δ = -352-4·20·2
Δ = 1065
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-\sqrt{1065}}{2*20}=\frac{35-\sqrt{1065}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{1065}}{2*20}=\frac{35+\sqrt{1065}}{40}
$