2/5x+6=12-2x

Solution for 2/5x+6=12-2x equation:

2/5x+6=12-2x

We move all terms to the left:

2/5x+6-(12-2x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

2/5x-(-2x+12)+6=0

We get rid of parentheses

2/5x+2x-12+6=0

We multiply all the terms by the denominator


2x*5x-12*5x+6*5x+2=0

Wy multiply elements

10x^2-60x+30x+2=0

We add all the numbers together, and all the variables

10x^2-30x+2=0

a = 10; b = -30; c = +2;
Δ = b2-4ac
Δ = -302-4·10·2
Δ = 820
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:

$\sqrt{\Delta}=\sqrt{820}=\sqrt{4*205}=\sqrt{4}*\sqrt{205}=2\sqrt{205}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{205}}{2*10}=\frac{30-2\sqrt{205}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{205}}{2*10}=\frac{30+2\sqrt{205}}{20}
$