4x^2+7x-21=24-4x

Solution for 4x^2+7x-21=24-4x equation:

4x^2+7x-21=24-4x

We move all terms to the left:

4x^2+7x-21-(24-4x)=0

We add all the numbers together, and all the variables

4x^2+7x-(-4x+24)-21=0

We get rid of parentheses

4x^2+7x+4x-24-21=0

We add all the numbers together, and all the variables

4x^2+11x-45=0

a = 4; b = 11; c = -45;
Δ = b2-4ac
Δ = 112-4·4·(-45)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-29}{2*4}=\frac{-40}{8}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+29}{2*4}=\frac{18}{8}
=2+1/4
$