6(x)(2.5x)=2160

Solution for 6(x)(2.5x)=2160 equation:

6(x)(2.5x)=2160

We move all terms to the left:

6(x)(2.5x)-(2160)=0

We add all the numbers together, and all the variables

6x(+2.5x)-2160=0

We multiply parentheses

12x^2-2160=0

a = 12; b = 0; c = -2160;
Δ = b2-4ac
Δ = 02-4·12·(-2160)
Δ = 103680
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:

$\sqrt{\Delta}=\sqrt{103680}=\sqrt{20736*5}=\sqrt{20736}*\sqrt{5}=144\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-144\sqrt{5}}{2*12}=\frac{0-144\sqrt{5}}{24}
=-\frac{144\sqrt{5}}{24}
=-6\sqrt{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+144\sqrt{5}}{2*12}=\frac{0+144\sqrt{5}}{24}
=\frac{144\sqrt{5}}{24}
=6\sqrt{5}
$