21x-4x^2=4x^2-9

Solution for 21x-4x^2=4x^2-9 equation:

21x-4x^2=4x^2-9

We move all terms to the left:

21x-4x^2-(4x^2-9)=0

We get rid of parentheses

-4x^2-4x^2+21x+9=0

We add all the numbers together, and all the variables

-8x^2+21x+9=0

a = -8; b = 21; c = +9;
Δ = b2-4ac
Δ = 212-4·(-8)·9
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-27}{2*-8}=\frac{-48}{-16}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+27}{2*-8}=\frac{6}{-16}
=-3/8
$