21-7(19-x2+6)-3x2+1=0

Solution for 21-7(19-x2+6)-3x2+1=0 equation:

21-7(19-x2+6)-3x^2+1=0

We add all the numbers together, and all the variables

-3x^2-7(-1x^2+19+6)+21+1=0

We add all the numbers together, and all the variables

-3x^2-7(-1x^2+19+6)+22=0

We multiply parentheses

-3x^2+7x^2-133-42+22=0

We add all the numbers together, and all the variables

4x^2-153=0

a = 4; b = 0; c = -153;
Δ = b2-4ac
Δ = 02-4·4·(-153)
Δ = 2448
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:

$\sqrt{\Delta}=\sqrt{2448}=\sqrt{144*17}=\sqrt{144}*\sqrt{17}=12\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{17}}{2*4}=\frac{0-12\sqrt{17}}{8}
=-\frac{12\sqrt{17}}{8}
=-\frac{3\sqrt{17}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{17}}{2*4}=\frac{0+12\sqrt{17}}{8}
=\frac{12\sqrt{17}}{8}
=\frac{3\sqrt{17}}{2}
$