(8/3)x-(9/4)x=-5/12

Solution for (8/3)x-(9/4)x=-5/12 equation:

(8/3)x-(9/4)x=-5/12

We move all terms to the left:

(8/3)x-(9/4)x-(-5/12)=0


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 4)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+8/3)x-(+9/4)x-(-5/12)=0

We multiply parentheses

8x^2-9x^2-(-5/12)=0

We get rid of parentheses

8x^2-9x^2+5/12=0

We multiply all the terms by the denominator


8x^2*12-9x^2*12+5=0

Wy multiply elements

96x^2-108x^2+5=0

We add all the numbers together, and all the variables

-12x^2+5=0

a = -12; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-12)·5
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{15}}{2*-12}=\frac{0-4\sqrt{15}}{-24}
=-\frac{4\sqrt{15}}{-24}
=-\frac{\sqrt{15}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{15}}{2*-12}=\frac{0+4\sqrt{15}}{-24}
=\frac{4\sqrt{15}}{-24}
=\frac{\sqrt{15}}{-6}
$