4x+13=9-3(x+9);x=-7

Solution for 4x+13=9-3(x+9);x=-7 equation:

4x+13=9-3(x+9)x=-7

We move all terms to the left:

4x+13-(9-3(x+9)x)=0


We calculate terms in parentheses: -(9-3(x+9)x), so:

9-3(x+9)x

determiningTheFunctionDomain
-3(x+9)x+9

We multiply parentheses

-3x^2-27x+9

Back to the equation:

-(-3x^2-27x+9)


We get rid of parentheses

3x^2+27x+4x-9+13=0

We add all the numbers together, and all the variables

3x^2+31x+4=0

a = 3; b = 31; c = +4;
Δ = b2-4ac
Δ = 312-4·3·4
Δ = 913
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{913}}{2*3}=\frac{-31-\sqrt{913}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+\sqrt{913}}{2*3}=\frac{-31+\sqrt{913}}{6}
$