x-4/15x=12

Solution for x-4/15x=12 equation:

x-4/15x=12

We move all terms to the left:

x-4/15x-(12)=0


Domain of the equation: 15x!=0

x!=0/15

x!=0

x∈R


We multiply all the terms by the denominator


x*15x-12*15x-4=0

Wy multiply elements

15x^2-180x-4=0

a = 15; b = -180; c = -4;
Δ = b2-4ac
Δ = -1802-4·15·(-4)
Δ = 32640
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:

$\sqrt{\Delta}=\sqrt{32640}=\sqrt{64*510}=\sqrt{64}*\sqrt{510}=8\sqrt{510}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-8\sqrt{510}}{2*15}=\frac{180-8\sqrt{510}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+8\sqrt{510}}{2*15}=\frac{180+8\sqrt{510}}{30}
$