5a-20a(4a-5a-7)=0

Solution for 5a-20a(4a-5a-7)=0 equation:

5a-20a(4a-5a-7)=0

We add all the numbers together, and all the variables

5a-20a(-1a-7)=0

We multiply parentheses

20a^2+5a+140a=0

We add all the numbers together, and all the variables

20a^2+145a=0

a = 20; b = 145; c = 0;
Δ = b2-4ac
Δ = 1452-4·20·0
Δ = 21025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{21025}=145$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(145)-145}{2*20}=\frac{-290}{40}
=-7+1/4
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(145)+145}{2*20}=\frac{0}{40}
=0
$