(2/3)(5x)=3x+2

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

(2/3)(5x)=3x+2

We move all terms to the left:

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


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

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

10x^2-(3x+2)=0

We get rid of parentheses

10x^2-3x-2=0

a = 10; b = -3; c = -2;
Δ = b2-4ac
Δ = -32-4·10·(-2)
Δ = 89
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{89}}{2*10}=\frac{3-\sqrt{89}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{89}}{2*10}=\frac{3+\sqrt{89}}{20}
$