6x(-47/9)+5x(71/3)=8

Solution for 6x(-47/9)+5x(71/3)=8 equation:

6x(-47/9)+5x(71/3)=8

We move all terms to the left:

6x(-47/9)+5x(71/3)-(8)=0

We add all the numbers together, and all the variables

6x(-47/9)+5x(+71/3)-8=0

We multiply parentheses

-282x^2+355x^2-8=0

We add all the numbers together, and all the variables

73x^2-8=0

a = 73; b = 0; c = -8;
Δ = b2-4ac
Δ = 02-4·73·(-8)
Δ = 2336
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:

$\sqrt{\Delta}=\sqrt{2336}=\sqrt{16*146}=\sqrt{16}*\sqrt{146}=4\sqrt{146}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{146}}{2*73}=\frac{0-4\sqrt{146}}{146}
=-\frac{4\sqrt{146}}{146}
=-\frac{2\sqrt{146}}{73}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{146}}{2*73}=\frac{0+4\sqrt{146}}{146}
=\frac{4\sqrt{146}}{146}
=\frac{2\sqrt{146}}{73}
$