x-3=(4/3)(2-x)+6

Solution for x-3=(4/3)(2-x)+6 equation:

x-3=(4/3)(2-x)+6

We move all terms to the left:

x-3-((4/3)(2-x)+6)=0


Domain of the equation: 3)(2-x)+6)!=0

x∈R


We add all the numbers together, and all the variables

x-((+4/3)(-1x+2)+6)-3=0

We multiply parentheses ..

-((-4x^2+4/3*2)+6)+x-3=0

We multiply all the terms by the denominator


-((-4x^2+4+x*3*2)+6)-3*3*2)+6)=0


We calculate terms in parentheses: -((-4x^2+4+x*3*2)+6), so:

(-4x^2+4+x*3*2)+6

We get rid of parentheses

-4x^2+x*3*2+4+6

We add all the numbers together, and all the variables

-4x^2+x*3*2+10

Wy multiply elements

-4x^2+6x*2+10

Wy multiply elements

-4x^2+12x+10

Back to the equation:

-(-4x^2+12x+10)


We add all the numbers together, and all the variables

-(-4x^2+12x+10)=0

We get rid of parentheses

4x^2-12x-10=0

a = 4; b = -12; c = -10;
Δ = b2-4ac
Δ = -122-4·4·(-10)
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{19}}{2*4}=\frac{12-4\sqrt{19}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{19}}{2*4}=\frac{12+4\sqrt{19}}{8}
$