2x(4/5x+x)=54

Solution for 2x(4/5x+x)=54 equation:

2x(4/5x+x)=54

We move all terms to the left:

2x(4/5x+x)-(54)=0


Domain of the equation: 5x+x)!=0

x∈R


We add all the numbers together, and all the variables

2x(+x+4/5x)-54=0

We multiply parentheses

2x^2+8x^2-54=0

We add all the numbers together, and all the variables

10x^2-54=0

a = 10; b = 0; c = -54;
Δ = b2-4ac
Δ = 02-4·10·(-54)
Δ = 2160
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:

$\sqrt{\Delta}=\sqrt{2160}=\sqrt{144*15}=\sqrt{144}*\sqrt{15}=12\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{15}}{2*10}=\frac{0-12\sqrt{15}}{20}
=-\frac{12\sqrt{15}}{20}
=-\frac{3\sqrt{15}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{15}}{2*10}=\frac{0+12\sqrt{15}}{20}
=\frac{12\sqrt{15}}{20}
=\frac{3\sqrt{15}}{5}
$