(7)(7+17)=(8x)(8x+13x)

Solution for (7)(7+17)=(8x)(8x+13x) equation:

(7)(7+17)=(8x)(8x+13x)

We move all terms to the left:

(7)(7+17)-((8x)(8x+13x))=0

We add all the numbers together, and all the variables

-(8x(+21x))+724=0


We calculate terms in parentheses: -(8x(+21x)), so:

8x(+21x)

We multiply parentheses

168x^2

Back to the equation:

-(168x^2)


a = -168; b = 0; c = +724;
Δ = b2-4ac
Δ = 02-4·(-168)·724
Δ = 486528
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:

$\sqrt{\Delta}=\sqrt{486528}=\sqrt{64*7602}=\sqrt{64}*\sqrt{7602}=8\sqrt{7602}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{7602}}{2*-168}=\frac{0-8\sqrt{7602}}{-336}
=-\frac{8\sqrt{7602}}{-336}
=-\frac{\sqrt{7602}}{-42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{7602}}{2*-168}=\frac{0+8\sqrt{7602}}{-336}
=\frac{8\sqrt{7602}}{-336}
=\frac{\sqrt{7602}}{-42}
$