6x2-10=278

Solution for 6x2-10=278 equation:

6x^2-10=278

We move all terms to the left:

6x^2-10-(278)=0

We add all the numbers together, and all the variables

6x^2-288=0

a = 6; b = 0; c = -288;
Δ = b2-4ac
Δ = 02-4·6·(-288)
Δ = 6912
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:

$\sqrt{\Delta}=\sqrt{6912}=\sqrt{2304*3}=\sqrt{2304}*\sqrt{3}=48\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48\sqrt{3}}{2*6}=\frac{0-48\sqrt{3}}{12}
=-\frac{48\sqrt{3}}{12}
=-4\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48\sqrt{3}}{2*6}=\frac{0+48\sqrt{3}}{12}
=\frac{48\sqrt{3}}{12}
=4\sqrt{3}
$