4/5x-1x=-12

Solution for 4/5x-1x=-12 equation:

4/5x-1x=-12

We move all terms to the left:

4/5x-1x-(-12)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+4/5x+12=0

We multiply all the terms by the denominator


-1x*5x+12*5x+4=0

Wy multiply elements

-5x^2+60x+4=0

a = -5; b = 60; c = +4;
Δ = b2-4ac
Δ = 602-4·(-5)·4
Δ = 3680
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:

$\sqrt{\Delta}=\sqrt{3680}=\sqrt{16*230}=\sqrt{16}*\sqrt{230}=4\sqrt{230}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-4\sqrt{230}}{2*-5}=\frac{-60-4\sqrt{230}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+4\sqrt{230}}{2*-5}=\frac{-60+4\sqrt{230}}{-10}
$