2x^2-65x^2+784=0

Solution for 2x^2-65x^2+784=0 equation:

2x^2-65x^2+784=0

We add all the numbers together, and all the variables

-63x^2+784=0

a = -63; b = 0; c = +784;
Δ = b2-4ac
Δ = 02-4·(-63)·784
Δ = 197568
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:

$\sqrt{\Delta}=\sqrt{197568}=\sqrt{28224*7}=\sqrt{28224}*\sqrt{7}=168\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-168\sqrt{7}}{2*-63}=\frac{0-168\sqrt{7}}{-126}
=-\frac{168\sqrt{7}}{-126}
=-\frac{4\sqrt{7}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+168\sqrt{7}}{2*-63}=\frac{0+168\sqrt{7}}{-126}
=\frac{168\sqrt{7}}{-126}
=\frac{4\sqrt{7}}{-3}
$