1/4(x)+1/6(x)=1

Solution for 1/4(x)+1/6(x)=1 equation:

1/4(x)+1/6(x)=1

We move all terms to the left:

1/4(x)+1/6(x)-(1)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We calculate fractions


6x/24x^2+4x/24x^2-1=0

We multiply all the terms by the denominator


6x+4x-1*24x^2=0

We add all the numbers together, and all the variables

10x-1*24x^2=0

Wy multiply elements

-24x^2+10x=0

a = -24; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-24)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-24}=\frac{-20}{-48}
=5/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-24}=\frac{0}{-48}
=0
$