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

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

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

We move all terms to the left:

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

We multiply parentheses

4x^2+84x-(-3(x-7))=0


We calculate terms in parentheses: -(-3(x-7)), so:

-3(x-7)

We multiply parentheses

-3x+21

Back to the equation:

-(-3x+21)


We get rid of parentheses

4x^2+84x+3x-21=0

We add all the numbers together, and all the variables

4x^2+87x-21=0

a = 4; b = 87; c = -21;
Δ = b2-4ac
Δ = 872-4·4·(-21)
Δ = 7905
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(87)-\sqrt{7905}}{2*4}=\frac{-87-\sqrt{7905}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(87)+\sqrt{7905}}{2*4}=\frac{-87+\sqrt{7905}}{8}
$