(7/5)x=5/8

Solution for (7/5)x=5/8 equation:

(7/5)x=5/8

We move all terms to the left:

(7/5)x-(5/8)=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-(+5/8)=0

We multiply parentheses

7x^2-(+5/8)=0

We get rid of parentheses

7x^2-5/8=0

We multiply all the terms by the denominator


7x^2*8-5=0

Wy multiply elements

56x^2-5=0

a = 56; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·56·(-5)
Δ = 1120
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:

$\sqrt{\Delta}=\sqrt{1120}=\sqrt{16*70}=\sqrt{16}*\sqrt{70}=4\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{70}}{2*56}=\frac{0-4\sqrt{70}}{112}
=-\frac{4\sqrt{70}}{112}
=-\frac{\sqrt{70}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{70}}{2*56}=\frac{0+4\sqrt{70}}{112}
=\frac{4\sqrt{70}}{112}
=\frac{\sqrt{70}}{28}
$