3/8x-5/12x=69

Solution for 3/8x-5/12x=69 equation:

3/8x-5/12x=69

We move all terms to the left:

3/8x-5/12x-(69)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R


We calculate fractions


36x/96x^2+(-40x)/96x^2-69=0

We multiply all the terms by the denominator


36x+(-40x)-69*96x^2=0

Wy multiply elements

-6624x^2+36x+(-40x)=0

We get rid of parentheses

-6624x^2+36x-40x=0

We add all the numbers together, and all the variables

-6624x^2-4x=0

a = -6624; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-6624)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-6624}=\frac{0}{-13248}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-6624}=\frac{8}{-13248}
=-1/1656
$