274x^2-40=0

Solution for 274x^2-40=0 equation:

274x^2-40=0

a = 274; b = 0; c = -40;
Δ = b2-4ac
Δ = 02-4·274·(-40)
Δ = 43840
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:

$\sqrt{\Delta}=\sqrt{43840}=\sqrt{64*685}=\sqrt{64}*\sqrt{685}=8\sqrt{685}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{685}}{2*274}=\frac{0-8\sqrt{685}}{548}
=-\frac{8\sqrt{685}}{548}
=-\frac{2\sqrt{685}}{137}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{685}}{2*274}=\frac{0+8\sqrt{685}}{548}
=\frac{8\sqrt{685}}{548}
=\frac{2\sqrt{685}}{137}
$