2/3x+7=-0.2x+3

Solution for 2/3x+7=-0.2x+3 equation:

2/3x+7=-0.2x+3

We move all terms to the left:

2/3x+7-(-0.2x+3)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x+0.2x-3+7=0

We multiply all the terms by the denominator


(0.2x)*3x-3*3x+7*3x+2=0

We add all the numbers together, and all the variables

(+0.2x)*3x-3*3x+7*3x+2=0

We multiply parentheses

0x^2-3*3x+7*3x+2=0

Wy multiply elements

0x^2-9x+21x+2=0

We add all the numbers together, and all the variables

x^2+12x+2=0

a = 1; b = 12; c = +2;
Δ = b2-4ac
Δ = 122-4·1·2
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{34}}{2*1}=\frac{-12-2\sqrt{34}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{34}}{2*1}=\frac{-12+2\sqrt{34}}{2}
$