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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


determiningTheFunctionDomain
3/2x-37x+5=0

We add all the numbers together, and all the variables

-37x+3/2x+5=0

We multiply all the terms by the denominator


-37x*2x+5*2x+3=0

Wy multiply elements

-74x^2+10x+3=0

a = -74; b = 10; c = +3;
Δ = b2-4ac
Δ = 102-4·(-74)·3
Δ = 988
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:

$\sqrt{\Delta}=\sqrt{988}=\sqrt{4*247}=\sqrt{4}*\sqrt{247}=2\sqrt{247}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{247}}{2*-74}=\frac{-10-2\sqrt{247}}{-148}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{247}}{2*-74}=\frac{-10+2\sqrt{247}}{-148}
$