(3x-15)(7x+21)=0

Solution for (3x-15)(7x+21)=0 equation:

(3x-15)(7x+21)=0

We multiply parentheses ..

(+21x^2+63x-105x-315)=0

We get rid of parentheses

21x^2+63x-105x-315=0

We add all the numbers together, and all the variables

21x^2-42x-315=0

a = 21; b = -42; c = -315;
Δ = b2-4ac
Δ = -422-4·21·(-315)
Δ = 28224
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{28224}=168$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-168}{2*21}=\frac{-126}{42}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+168}{2*21}=\frac{210}{42}
=5
$