2(x*x)-13-84=0

Solution for 2(x*x)-13-84=0 equation:

2(x*x)-13-84=0

We add all the numbers together, and all the variables

2(+x*x)-13-84=0

We add all the numbers together, and all the variables

2(+x*x)-97=0

We multiply parentheses

2x^2-97=0

a = 2; b = 0; c = -97;
Δ = b2-4ac
Δ = 02-4·2·(-97)
Δ = 776
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:

$\sqrt{\Delta}=\sqrt{776}=\sqrt{4*194}=\sqrt{4}*\sqrt{194}=2\sqrt{194}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{194}}{2*2}=\frac{0-2\sqrt{194}}{4}
=-\frac{2\sqrt{194}}{4}
=-\frac{\sqrt{194}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{194}}{2*2}=\frac{0+2\sqrt{194}}{4}
=\frac{2\sqrt{194}}{4}
=\frac{\sqrt{194}}{2}
$