-1=4(3-x2)

Solution for -1=4(3-x2) equation:

-1=4(3-x2)

We move all terms to the left:

-1-(4(3-x2))=0

We add all the numbers together, and all the variables

-(4(-1x^2+3))-1=0


We calculate terms in parentheses: -(4(-1x^2+3)), so:

4(-1x^2+3)

We multiply parentheses

-4x^2+12

Back to the equation:

-(-4x^2+12)


We get rid of parentheses

4x^2-12-1=0

We add all the numbers together, and all the variables

4x^2-13=0

a = 4; b = 0; c = -13;
Δ = b2-4ac
Δ = 02-4·4·(-13)
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{13}}{2*4}=\frac{0-4\sqrt{13}}{8}
=-\frac{4\sqrt{13}}{8}
=-\frac{\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{13}}{2*4}=\frac{0+4\sqrt{13}}{8}
=\frac{4\sqrt{13}}{8}
=\frac{\sqrt{13}}{2}
$