5x(8x+3x)=2(55)

Solution for 5x(8x+3x)=2(55) equation:

5x(8x+3x)=2(55)

We move all terms to the left:

5x(8x+3x)-(2(55))=0

determiningTheFunctionDomain
5x(8x+3x)-255=0

We add all the numbers together, and all the variables

5x(+11x)-255=0

We multiply parentheses

55x^2-255=0

a = 55; b = 0; c = -255;
Δ = b2-4ac
Δ = 02-4·55·(-255)
Δ = 56100
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:

$\sqrt{\Delta}=\sqrt{56100}=\sqrt{100*561}=\sqrt{100}*\sqrt{561}=10\sqrt{561}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{561}}{2*55}=\frac{0-10\sqrt{561}}{110}
=-\frac{10\sqrt{561}}{110}
=-\frac{\sqrt{561}}{11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{561}}{2*55}=\frac{0+10\sqrt{561}}{110}
=\frac{10\sqrt{561}}{110}
=\frac{\sqrt{561}}{11}
$