5x+18=1/2*7x

Solution for 5x+18=1/2*7x equation:

5x+18=1/2*7x

We move all terms to the left:

5x+18-(1/2*7x)=0


Domain of the equation: 2*7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5x-(+1/2*7x)+18=0

We get rid of parentheses

5x-1/2*7x+18=0

We multiply all the terms by the denominator


5x*2*7x+18*2*7x-1=0

Wy multiply elements

70x^2*7+252x*7-1=0

Wy multiply elements

490x^2+1764x-1=0

a = 490; b = 1764; c = -1;
Δ = b2-4ac
Δ = 17642-4·490·(-1)
Δ = 3113656
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:

$\sqrt{\Delta}=\sqrt{3113656}=\sqrt{33124*94}=\sqrt{33124}*\sqrt{94}=182\sqrt{94}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1764)-182\sqrt{94}}{2*490}=\frac{-1764-182\sqrt{94}}{980}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1764)+182\sqrt{94}}{2*490}=\frac{-1764+182\sqrt{94}}{980}
$