5a-4a(3a+7)=-21

Solution for 5a-4a(3a+7)=-21 equation:

5a-4a(3a+7)=-21

We move all terms to the left:

5a-4a(3a+7)-(-21)=0

We add all the numbers together, and all the variables

5a-4a(3a+7)+21=0

We multiply parentheses

-12a^2+5a-28a+21=0

We add all the numbers together, and all the variables

-12a^2-23a+21=0

a = -12; b = -23; c = +21;
Δ = b2-4ac
Δ = -232-4·(-12)·21
Δ = 1537
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-\sqrt{1537}}{2*-12}=\frac{23-\sqrt{1537}}{-24}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{1537}}{2*-12}=\frac{23+\sqrt{1537}}{-24}
$