1^4-18x^2+77=0

Solution for 1^4-18x^2+77=0 equation:

1^4-18x^2+77=0

We add all the numbers together, and all the variables

-18x^2+78=0

a = -18; b = 0; c = +78;
Δ = b2-4ac
Δ = 02-4·(-18)·78
Δ = 5616
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:

$\sqrt{\Delta}=\sqrt{5616}=\sqrt{144*39}=\sqrt{144}*\sqrt{39}=12\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{39}}{2*-18}=\frac{0-12\sqrt{39}}{-36}
=-\frac{12\sqrt{39}}{-36}
=-\frac{\sqrt{39}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{39}}{2*-18}=\frac{0+12\sqrt{39}}{-36}
=\frac{12\sqrt{39}}{-36}
=\frac{\sqrt{39}}{-3}
$