6-(2/3)(x+5)=4X

Solution for 6-(2/3)(x+5)=4X equation:

6-(2/3)(x+5)=4x

We move all terms to the left:

6-(2/3)(x+5)-(4x)=0


Domain of the equation: 3)(x+5)!=0

x∈R


We add all the numbers together, and all the variables

-(+2/3)(x+5)-4x+6=0

We add all the numbers together, and all the variables

-4x-(+2/3)(x+5)+6=0

We multiply parentheses ..

-(+2x^2+2/3*5)-4x+6=0

We multiply all the terms by the denominator


-(+2x^2+2-4x*3*5)+6*3*5)=0

We add all the numbers together, and all the variables

-(+2x^2+2-4x*3*5)=0

We get rid of parentheses

-2x^2+4x*3*5-2=0

Wy multiply elements

-2x^2+60x*5-2=0

Wy multiply elements

-2x^2+300x-2=0

a = -2; b = 300; c = -2;
Δ = b2-4ac
Δ = 3002-4·(-2)·(-2)
Δ = 89984
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:

$\sqrt{\Delta}=\sqrt{89984}=\sqrt{64*1406}=\sqrt{64}*\sqrt{1406}=8\sqrt{1406}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(300)-8\sqrt{1406}}{2*-2}=\frac{-300-8\sqrt{1406}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(300)+8\sqrt{1406}}{2*-2}=\frac{-300+8\sqrt{1406}}{-4}
$