6x^2-43.5=250

Solution for 6x^2-43.5=250 equation:

6x^2-43.5=250

We move all terms to the left:

6x^2-43.5-(250)=0

We add all the numbers together, and all the variables

6x^2-293.5=0

a = 6; b = 0; c = -293.5;
Δ = b2-4ac
Δ = 02-4·6·(-293.5)
Δ = 7044
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:

$\sqrt{\Delta}=\sqrt{7044}=\sqrt{4*1761}=\sqrt{4}*\sqrt{1761}=2\sqrt{1761}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{1761}}{2*6}=\frac{0-2\sqrt{1761}}{12}
=-\frac{2\sqrt{1761}}{12}
=-\frac{\sqrt{1761}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{1761}}{2*6}=\frac{0+2\sqrt{1761}}{12}
=\frac{2\sqrt{1761}}{12}
=\frac{\sqrt{1761}}{6}
$