(13/7)x-23=27

Solution for (13/7)x-23=27 equation:

(13/7)x-23=27

We move all terms to the left:

(13/7)x-23-(27)=0


Domain of the equation: 7)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+13/7)x-23-27=0

We add all the numbers together, and all the variables

(+13/7)x-50=0

We multiply parentheses

13x^2-50=0

a = 13; b = 0; c = -50;
Δ = b2-4ac
Δ = 02-4·13·(-50)
Δ = 2600
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:

$\sqrt{\Delta}=\sqrt{2600}=\sqrt{100*26}=\sqrt{100}*\sqrt{26}=10\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{26}}{2*13}=\frac{0-10\sqrt{26}}{26}
=-\frac{10\sqrt{26}}{26}
=-\frac{5\sqrt{26}}{13}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{26}}{2*13}=\frac{0+10\sqrt{26}}{26}
=\frac{10\sqrt{26}}{26}
=\frac{5\sqrt{26}}{13}
$