(3/2)x=5/7

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

(3/2)x=5/7

We move all terms to the left:

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


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

3x^2-5/7=0

We multiply all the terms by the denominator


3x^2*7-5=0

Wy multiply elements

21x^2-5=0

a = 21; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·21·(-5)
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{105}}{2*21}=\frac{0-2\sqrt{105}}{42}
=-\frac{2\sqrt{105}}{42}
=-\frac{\sqrt{105}}{21}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{105}}{2*21}=\frac{0+2\sqrt{105}}{42}
=\frac{2\sqrt{105}}{42}
=\frac{\sqrt{105}}{21}
$