21=4x^2+4x+-3

Solution for 21=4x^2+4x+-3 equation:

21=4x^2+4x+-3

We move all terms to the left:

21-(4x^2+4x+-3)=0

We use the square of the difference formula

-(4x^2+4x-3)+21=0

We get rid of parentheses

-4x^2-4x+3+21=0

We add all the numbers together, and all the variables

-4x^2-4x+24=0

a = -4; b = -4; c = +24;
Δ = b2-4ac
Δ = -42-4·(-4)·24
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-20}{2*-4}=\frac{-16}{-8}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+20}{2*-4}=\frac{24}{-8}
=-3
$