8x(8x+6x)=7(16)

Solution for 8x(8x+6x)=7(16) equation:

8x(8x+6x)=7(16)

We move all terms to the left:

8x(8x+6x)-(7(16))=0

determiningTheFunctionDomain
8x(8x+6x)-716=0

We add all the numbers together, and all the variables

8x(+14x)-716=0

We multiply parentheses

112x^2-716=0

a = 112; b = 0; c = -716;
Δ = b2-4ac
Δ = 02-4·112·(-716)
Δ = 320768
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:

$\sqrt{\Delta}=\sqrt{320768}=\sqrt{256*1253}=\sqrt{256}*\sqrt{1253}=16\sqrt{1253}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{1253}}{2*112}=\frac{0-16\sqrt{1253}}{224}
=-\frac{16\sqrt{1253}}{224}
=-\frac{\sqrt{1253}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{1253}}{2*112}=\frac{0+16\sqrt{1253}}{224}
=\frac{16\sqrt{1253}}{224}
=\frac{\sqrt{1253}}{14}
$