21a^2-47a=-20

Solution for 21a^2-47a=-20 equation:

21a^2-47a=-20

We move all terms to the left:

21a^2-47a-(-20)=0

We add all the numbers together, and all the variables

21a^2-47a+20=0

a = 21; b = -47; c = +20;
Δ = b2-4ac
Δ = -472-4·21·20
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-23}{2*21}=\frac{24}{42}
=4/7
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+23}{2*21}=\frac{70}{42}
=1+2/3
$