-4x(x+3)=7x+21

Solution for -4x(x+3)=7x+21 equation:

-4x(x+3)=7x+21

We move all terms to the left:

-4x(x+3)-(7x+21)=0

We multiply parentheses

-4x^2-12x-(7x+21)=0

We get rid of parentheses

-4x^2-12x-7x-21=0

We add all the numbers together, and all the variables

-4x^2-19x-21=0

a = -4; b = -19; c = -21;
Δ = b2-4ac
Δ = -192-4·(-4)·(-21)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-5}{2*-4}=\frac{14}{-8}
=-1+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+5}{2*-4}=\frac{24}{-8}
=-3
$