2/5x+21=-1.6x+5-2x

Solution for 2/5x+21=-1.6x+5-2x equation:

2/5x+21=-1.6x+5-2x

We move all terms to the left:

2/5x+21-(-1.6x+5-2x)=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-(-3.6x+5)+21=0

We get rid of parentheses

2/5x+3.6x-5+21=0

We multiply all the terms by the denominator


(3.6x)*5x-5*5x+21*5x+2=0

We add all the numbers together, and all the variables

(+3.6x)*5x-5*5x+21*5x+2=0

We multiply parentheses

15x^2-5*5x+21*5x+2=0

Wy multiply elements

15x^2-25x+105x+2=0

We add all the numbers together, and all the variables

15x^2+80x+2=0

a = 15; b = 80; c = +2;
Δ = b2-4ac
Δ = 802-4·15·2
Δ = 6280
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:

$\sqrt{\Delta}=\sqrt{6280}=\sqrt{4*1570}=\sqrt{4}*\sqrt{1570}=2\sqrt{1570}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-2\sqrt{1570}}{2*15}=\frac{-80-2\sqrt{1570}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+2\sqrt{1570}}{2*15}=\frac{-80+2\sqrt{1570}}{30}
$