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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

(+21x)*13x-(24*17)=0

We add all the numbers together, and all the variables

(+21x)*13x-408=0

We multiply parentheses

273x^2-408=0

a = 273; b = 0; c = -408;
Δ = b2-4ac
Δ = 02-4·273·(-408)
Δ = 445536
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:

$\sqrt{\Delta}=\sqrt{445536}=\sqrt{144*3094}=\sqrt{144}*\sqrt{3094}=12\sqrt{3094}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{3094}}{2*273}=\frac{0-12\sqrt{3094}}{546}
=-\frac{12\sqrt{3094}}{546}
=-\frac{2\sqrt{3094}}{91}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{3094}}{2*273}=\frac{0+12\sqrt{3094}}{546}
=\frac{12\sqrt{3094}}{546}
=\frac{2\sqrt{3094}}{91}
$