5(x^2-4x-21)=0

Solution for 5(x^2-4x-21)=0 equation:

5(x^2-4x-21)=0

We multiply parentheses

5x^2-20x-105=0

a = 5; b = -20; c = -105;
Δ = b2-4ac
Δ = -202-4·5·(-105)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-50}{2*5}=\frac{-30}{10}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+50}{2*5}=\frac{70}{10}
=7
$