2/3x+5=7x

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

2/3x+5=7x

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -21; b = 15; c = +2;
Δ = b2-4ac
Δ = 152-4·(-21)·2
Δ = 393
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{-(15)-\sqrt{393}}{2*-21}=\frac{-15-\sqrt{393}}{-42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{393}}{2*-21}=\frac{-15+\sqrt{393}}{-42}
$