2/5x-6x=15

Solution for 2/5x-6x=15 equation:

2/5x-6x=15

We move all terms to the left:

2/5x-6x-(15)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-6x+2/5x-15=0

We multiply all the terms by the denominator


-6x*5x-15*5x+2=0

Wy multiply elements

-30x^2-75x+2=0

a = -30; b = -75; c = +2;
Δ = b2-4ac
Δ = -752-4·(-30)·2
Δ = 5865
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-\sqrt{5865}}{2*-30}=\frac{75-\sqrt{5865}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+\sqrt{5865}}{2*-30}=\frac{75+\sqrt{5865}}{-60}
$