(x+7)(x+9)=7(8)

Solution for (x+7)(x+9)=7(8) equation:

(x+7)(x+9)=7(8)

We move all terms to the left:

(x+7)(x+9)-(7(8))=0

determiningTheFunctionDomain
(x+7)(x+9)-78=0

We multiply parentheses ..

(+x^2+9x+7x+63)-78=0

We get rid of parentheses

x^2+9x+7x+63-78=0

We add all the numbers together, and all the variables

x^2+16x-15=0

a = 1; b = 16; c = -15;
Δ = b2-4ac
Δ = 162-4·1·(-15)
Δ = 316
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:

$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{79}}{2*1}=\frac{-16-2\sqrt{79}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{79}}{2*1}=\frac{-16+2\sqrt{79}}{2}
$