18+3x-5=7x(-4-x)

Solution for 18+3x-5=7x(-4-x) equation:

18+3x-5=7x(-4-x)

We move all terms to the left:

18+3x-5-(7x(-4-x))=0

We add all the numbers together, and all the variables

3x-(7x(-1x-4))+18-5=0

We add all the numbers together, and all the variables

3x-(7x(-1x-4))+13=0


We calculate terms in parentheses: -(7x(-1x-4)), so:

7x(-1x-4)

We multiply parentheses

-7x^2-28x

Back to the equation:

-(-7x^2-28x)


We get rid of parentheses

7x^2+28x+3x+13=0

We add all the numbers together, and all the variables

7x^2+31x+13=0

a = 7; b = 31; c = +13;
Δ = b2-4ac
Δ = 312-4·7·13
Δ = 597
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-\sqrt{597}}{2*7}=\frac{-31-\sqrt{597}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+\sqrt{597}}{2*7}=\frac{-31+\sqrt{597}}{14}
$