2/5x+3+2x-12=15

Solution for 2/5x+3+2x-12=15 equation:

2/5x+3+2x-12=15

We move all terms to the left:

2/5x+3+2x-12-(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

2x+2/5x-24=0

We multiply all the terms by the denominator


2x*5x-24*5x+2=0

Wy multiply elements

10x^2-120x+2=0

a = 10; b = -120; c = +2;
Δ = b2-4ac
Δ = -1202-4·10·2
Δ = 14320
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:

$\sqrt{\Delta}=\sqrt{14320}=\sqrt{16*895}=\sqrt{16}*\sqrt{895}=4\sqrt{895}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-4\sqrt{895}}{2*10}=\frac{120-4\sqrt{895}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+4\sqrt{895}}{2*10}=\frac{120+4\sqrt{895}}{20}
$