6750=(10)(x)(2)

Solution for 6750=(10)(x)(2) equation:

6750=(10)(x)(2)

We move all terms to the left:

6750-((10)(x)(2))=0

determiningTheFunctionDomain
-10x2+6750=0

We add all the numbers together, and all the variables

-10x^2+6750=0

a = -10; b = 0; c = +6750;
Δ = b2-4ac
Δ = 02-4·(-10)·6750
Δ = 270000
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:

$\sqrt{\Delta}=\sqrt{270000}=\sqrt{90000*3}=\sqrt{90000}*\sqrt{3}=300\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-300\sqrt{3}}{2*-10}=\frac{0-300\sqrt{3}}{-20}
=-\frac{300\sqrt{3}}{-20}
=-\frac{15\sqrt{3}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+300\sqrt{3}}{2*-10}=\frac{0+300\sqrt{3}}{-20}
=\frac{300\sqrt{3}}{-20}
=\frac{15\sqrt{3}}{-1}
$