2(2.5)=3x(x+3x)

Solution for 2(2.5)=3x(x+3x) equation:

2(2.5)=3x(x+3x)

We move all terms to the left:

2(2.5)-(3x(x+3x))=0

We add all the numbers together, and all the variables

-(3x(+4x))+2(2.5)=0

We add all the numbers together, and all the variables

-(3x(+4x))+5=0


We calculate terms in parentheses: -(3x(+4x)), so:

3x(+4x)

We multiply parentheses

12x^2

Back to the equation:

-(12x^2)


a = -12; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-12)·5
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{15}}{2*-12}=\frac{0-4\sqrt{15}}{-24}
=-\frac{4\sqrt{15}}{-24}
=-\frac{\sqrt{15}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{15}}{2*-12}=\frac{0+4\sqrt{15}}{-24}
=\frac{4\sqrt{15}}{-24}
=\frac{\sqrt{15}}{-6}
$