4(2)-2x2+6(1)=0

Solution for 4(2)-2x2+6(1)=0 equation:

4(2)-2x^2+6(1)=0

We add all the numbers together, and all the variables

-2x^2+103=0

a = -2; b = 0; c = +103;
Δ = b2-4ac
Δ = 02-4·(-2)·103
Δ = 824
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:

$\sqrt{\Delta}=\sqrt{824}=\sqrt{4*206}=\sqrt{4}*\sqrt{206}=2\sqrt{206}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{206}}{2*-2}=\frac{0-2\sqrt{206}}{-4}
=-\frac{2\sqrt{206}}{-4}
=-\frac{\sqrt{206}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{206}}{2*-2}=\frac{0+2\sqrt{206}}{-4}
=\frac{2\sqrt{206}}{-4}
=\frac{\sqrt{206}}{-2}
$