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}
$