(7/5)x=7/15

Solution for (7/5)x=7/15 equation:

(7/5)x=7/15

We move all terms to the left:

(7/5)x-(7/15)=0


Domain of the equation: 5)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+7/5)x-(+7/15)=0

We multiply parentheses

7x^2-(+7/15)=0

We get rid of parentheses

7x^2-7/15=0

We multiply all the terms by the denominator


7x^2*15-7=0

Wy multiply elements

105x^2-7=0

a = 105; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·105·(-7)
Δ = 2940
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:

$\sqrt{\Delta}=\sqrt{2940}=\sqrt{196*15}=\sqrt{196}*\sqrt{15}=14\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{15}}{2*105}=\frac{0-14\sqrt{15}}{210}
=-\frac{14\sqrt{15}}{210}
=-\frac{\sqrt{15}}{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{15}}{2*105}=\frac{0+14\sqrt{15}}{210}
=\frac{14\sqrt{15}}{210}
=\frac{\sqrt{15}}{15}
$