78x2-25=1

Solution for 78x2-25=1 equation:

78x^2-25=1

We move all terms to the left:

78x^2-25-(1)=0

We add all the numbers together, and all the variables

78x^2-26=0

a = 78; b = 0; c = -26;
Δ = b2-4ac
Δ = 02-4·78·(-26)
Δ = 8112
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:

$\sqrt{\Delta}=\sqrt{8112}=\sqrt{2704*3}=\sqrt{2704}*\sqrt{3}=52\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-52\sqrt{3}}{2*78}=\frac{0-52\sqrt{3}}{156}
=-\frac{52\sqrt{3}}{156}
=-\frac{\sqrt{3}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+52\sqrt{3}}{2*78}=\frac{0+52\sqrt{3}}{156}
=\frac{52\sqrt{3}}{156}
=\frac{\sqrt{3}}{3}
$