2/3x+7=0.45x-11

Solution for 2/3x+7=0.45x-11 equation:

2/3x+7=0.45x-11

We move all terms to the left:

2/3x+7-(0.45x-11)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x-0.45x+11+7=0

We multiply all the terms by the denominator


-(0.45x)*3x+11*3x+7*3x+2=0

We add all the numbers together, and all the variables

-(+0.45x)*3x+11*3x+7*3x+2=0

We multiply parentheses

-0x^2+11*3x+7*3x+2=0

Wy multiply elements

-0x^2+33x+21x+2=0

We add all the numbers together, and all the variables

-1x^2+54x+2=0

a = -1; b = 54; c = +2;
Δ = b2-4ac
Δ = 542-4·(-1)·2
Δ = 2924
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:

$\sqrt{\Delta}=\sqrt{2924}=\sqrt{4*731}=\sqrt{4}*\sqrt{731}=2\sqrt{731}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-2\sqrt{731}}{2*-1}=\frac{-54-2\sqrt{731}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+2\sqrt{731}}{2*-1}=\frac{-54+2\sqrt{731}}{-2}
$