(2/5)x+3/7=12

Solution for (2/5)x+3/7=12 equation:

(2/5)x+3/7=12

We move all terms to the left:

(2/5)x+3/7-(12)=0


Domain of the equation: 5)x!=0

x!=0/1

x!=0

x∈R


determiningTheFunctionDomain
(2/5)x-12+3/7=0

We add all the numbers together, and all the variables

(+2/5)x-12+3/7=0

We multiply parentheses

2x^2-12+3/7=0

We multiply all the terms by the denominator


2x^2*7+3-12*7=0

We add all the numbers together, and all the variables

2x^2*7-81=0

Wy multiply elements

14x^2-81=0

a = 14; b = 0; c = -81;
Δ = b2-4ac
Δ = 02-4·14·(-81)
Δ = 4536
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:

$\sqrt{\Delta}=\sqrt{4536}=\sqrt{324*14}=\sqrt{324}*\sqrt{14}=18\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{14}}{2*14}=\frac{0-18\sqrt{14}}{28}
=-\frac{18\sqrt{14}}{28}
=-\frac{9\sqrt{14}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{14}}{2*14}=\frac{0+18\sqrt{14}}{28}
=\frac{18\sqrt{14}}{28}
=\frac{9\sqrt{14}}{14}
$