(2/3x)+4=5x

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

(2/3x)+4=5x

We move all terms to the left:

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


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-5x+2/3x+4=0

We multiply all the terms by the denominator


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

Wy multiply elements

-15x^2+12x+2=0

a = -15; b = 12; c = +2;
Δ = b2-4ac
Δ = 122-4·(-15)·2
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{66}}{2*-15}=\frac{-12-2\sqrt{66}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{66}}{2*-15}=\frac{-12+2\sqrt{66}}{-30}
$