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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

8x(+17x)-(716)=0

We add all the numbers together, and all the variables

8x(+17x)-716=0

We multiply parentheses

136x^2-716=0

a = 136; b = 0; c = -716;
Δ = b2-4ac
Δ = 02-4·136·(-716)
Δ = 389504
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:

$\sqrt{\Delta}=\sqrt{389504}=\sqrt{64*6086}=\sqrt{64}*\sqrt{6086}=8\sqrt{6086}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{6086}}{2*136}=\frac{0-8\sqrt{6086}}{272}
=-\frac{8\sqrt{6086}}{272}
=-\frac{\sqrt{6086}}{34}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{6086}}{2*136}=\frac{0+8\sqrt{6086}}{272}
=\frac{8\sqrt{6086}}{272}
=\frac{\sqrt{6086}}{34}
$