1/4x+1/3x=1/2+10

Solution for 1/4x+1/3x=1/2+10 equation:

1/4x+1/3x=1/2+10

We move all terms to the left:

1/4x+1/3x-(1/2+10)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/4x+1/3x-10-1/2=0

We calculate fractions


(-36x^2)/48x^2+12x/48x^2+16x/48x^2-10=0

We multiply all the terms by the denominator


(-36x^2)+12x+16x-10*48x^2=0

We add all the numbers together, and all the variables

(-36x^2)+28x-10*48x^2=0

Wy multiply elements

(-36x^2)-480x^2+28x=0

We get rid of parentheses

-36x^2-480x^2+28x=0

We add all the numbers together, and all the variables

-516x^2+28x=0

a = -516; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·(-516)·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28}{2*-516}=\frac{-56}{-1032}
=7/129
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*-516}=\frac{0}{-1032}
=0
$