(4/7)x-5=13

Solution for (4/7)x-5=13 equation:

(4/7)x-5=13

We move all terms to the left:

(4/7)x-5-(13)=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

(+4/7)x-5-13=0

We add all the numbers together, and all the variables

(+4/7)x-18=0

We multiply parentheses

4x^2-18=0

a = 4; b = 0; c = -18;
Δ = b2-4ac
Δ = 02-4·4·(-18)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{2}}{2*4}=\frac{0-12\sqrt{2}}{8}
=-\frac{12\sqrt{2}}{8}
=-\frac{3\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{2}}{2*4}=\frac{0+12\sqrt{2}}{8}
=\frac{12\sqrt{2}}{8}
=\frac{3\sqrt{2}}{2}
$