2/3x+7=5x-2

Solution for 2/3x+7=5x-2 equation:

2/3x+7=5x-2

We move all terms to the left:

2/3x+7-(5x-2)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x-5x+2+7=0

We multiply all the terms by the denominator


-5x*3x+2*3x+7*3x+2=0

Wy multiply elements

-15x^2+6x+21x+2=0

We add all the numbers together, and all the variables

-15x^2+27x+2=0

a = -15; b = 27; c = +2;
Δ = b2-4ac
Δ = 272-4·(-15)·2
Δ = 849
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{-(27)-\sqrt{849}}{2*-15}=\frac{-27-\sqrt{849}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+\sqrt{849}}{2*-15}=\frac{-27+\sqrt{849}}{-30}
$