18+3x-5=7x(-14-x)

Solution for 18+3x-5=7x(-14-x) equation:

18+3x-5=7x(-14-x)

We move all terms to the left:

18+3x-5-(7x(-14-x))=0

We add all the numbers together, and all the variables

3x-(7x(-1x-14))+18-5=0

We add all the numbers together, and all the variables

3x-(7x(-1x-14))+13=0


We calculate terms in parentheses: -(7x(-1x-14)), so:

7x(-1x-14)

We multiply parentheses

-7x^2-98x

Back to the equation:

-(-7x^2-98x)


We get rid of parentheses

7x^2+98x+3x+13=0

We add all the numbers together, and all the variables

7x^2+101x+13=0

a = 7; b = 101; c = +13;
Δ = b2-4ac
Δ = 1012-4·7·13
Δ = 9837
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:

$\sqrt{\Delta}=\sqrt{9837}=\sqrt{9*1093}=\sqrt{9}*\sqrt{1093}=3\sqrt{1093}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(101)-3\sqrt{1093}}{2*7}=\frac{-101-3\sqrt{1093}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(101)+3\sqrt{1093}}{2*7}=\frac{-101+3\sqrt{1093}}{14}
$