5/3x=2x-7

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

5/3x=2x-7

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

5/3x-2x+7=0

We multiply all the terms by the denominator


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

Wy multiply elements

-6x^2+21x+5=0

a = -6; b = 21; c = +5;
Δ = b2-4ac
Δ = 212-4·(-6)·5
Δ = 561
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{-(21)-\sqrt{561}}{2*-6}=\frac{-21-\sqrt{561}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{561}}{2*-6}=\frac{-21+\sqrt{561}}{-12}
$