(7/12x)-(x)=-5

Solution for (7/12x)-(x)=-5 equation:

(7/12x)-(x)=-5

We move all terms to the left:

(7/12x)-(x)-(-5)=0


Domain of the equation: 12x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+7/12x)-x-(-5)=0

We add all the numbers together, and all the variables

-1x+(+7/12x)+5=0

We get rid of parentheses

-1x+7/12x+5=0

We multiply all the terms by the denominator


-1x*12x+5*12x+7=0

Wy multiply elements

-12x^2+60x+7=0

a = -12; b = 60; c = +7;
Δ = b2-4ac
Δ = 602-4·(-12)·7
Δ = 3936
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:

$\sqrt{\Delta}=\sqrt{3936}=\sqrt{16*246}=\sqrt{16}*\sqrt{246}=4\sqrt{246}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-4\sqrt{246}}{2*-12}=\frac{-60-4\sqrt{246}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+4\sqrt{246}}{2*-12}=\frac{-60+4\sqrt{246}}{-24}
$