(x+7)(x+9)=4x+31(x+7)(x+9)=4x+31

Solution for (x+7)(x+9)=4x+31(x+7)(x+9)=4x+31 equation:

(x+7)(x+9)=4x+31(x+7)(x+9)=4x+31

We move all terms to the left:

(x+7)(x+9)-(4x+31(x+7)(x+9))=0

We multiply parentheses ..

(+x^2+9x+7x+63)-(4x+31(+x^2+9x+7x+63))=0


We calculate terms in parentheses: -(4x+31(+x^2+9x+7x+63)), so:

4x+31(+x^2+9x+7x+63)

determiningTheFunctionDomain
31(+x^2+9x+7x+63)+4x

We multiply parentheses

31x^2+279x+217x+4x+1953

We add all the numbers together, and all the variables

31x^2+500x+1953

Back to the equation:

-(31x^2+500x+1953)


We get rid of parentheses

x^2-31x^2+9x+7x-500x+63-1953=0

We add all the numbers together, and all the variables

-30x^2-484x-1890=0

a = -30; b = -484; c = -1890;
Δ = b2-4ac
Δ = -4842-4·(-30)·(-1890)
Δ = 7456
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:

$\sqrt{\Delta}=\sqrt{7456}=\sqrt{16*466}=\sqrt{16}*\sqrt{466}=4\sqrt{466}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-484)-4\sqrt{466}}{2*-30}=\frac{484-4\sqrt{466}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-484)+4\sqrt{466}}{2*-30}=\frac{484+4\sqrt{466}}{-60}
$