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

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

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

We move all terms to the left:

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


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-5x^2+30x+75x+2=0

We add all the numbers together, and all the variables

-5x^2+105x+2=0

a = -5; b = 105; c = +2;
Δ = b2-4ac
Δ = 1052-4·(-5)·2
Δ = 11065
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{-(105)-\sqrt{11065}}{2*-5}=\frac{-105-\sqrt{11065}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(105)+\sqrt{11065}}{2*-5}=\frac{-105+\sqrt{11065}}{-10}
$