2x^2+18=643

Solution for 2x^2+18=643 equation:

2x^2+18=643

We move all terms to the left:

2x^2+18-(643)=0

We add all the numbers together, and all the variables

2x^2-625=0

a = 2; b = 0; c = -625;
Δ = b2-4ac
Δ = 02-4·2·(-625)
Δ = 5000
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:

$\sqrt{\Delta}=\sqrt{5000}=\sqrt{2500*2}=\sqrt{2500}*\sqrt{2}=50\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-50\sqrt{2}}{2*2}=\frac{0-50\sqrt{2}}{4}
=-\frac{50\sqrt{2}}{4}
=-\frac{25\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+50\sqrt{2}}{2*2}=\frac{0+50\sqrt{2}}{4}
=\frac{50\sqrt{2}}{4}
=\frac{25\sqrt{2}}{2}
$