4x2-12-65=0

Solution for 4x2-12-65=0 equation:

4x^2-12-65=0

We add all the numbers together, and all the variables

4x^2-77=0

a = 4; b = 0; c = -77;
Δ = b2-4ac
Δ = 02-4·4·(-77)
Δ = 1232
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:

$\sqrt{\Delta}=\sqrt{1232}=\sqrt{16*77}=\sqrt{16}*\sqrt{77}=4\sqrt{77}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{77}}{2*4}=\frac{0-4\sqrt{77}}{8}
=-\frac{4\sqrt{77}}{8}
=-\frac{\sqrt{77}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{77}}{2*4}=\frac{0+4\sqrt{77}}{8}
=\frac{4\sqrt{77}}{8}
=\frac{\sqrt{77}}{2}
$