(4x-5)(7x+21)=0

Solution for (4x-5)(7x+21)=0 equation:

(4x-5)(7x+21)=0

We multiply parentheses ..

(+28x^2+84x-35x-105)=0

We get rid of parentheses

28x^2+84x-35x-105=0

We add all the numbers together, and all the variables

28x^2+49x-105=0

a = 28; b = 49; c = -105;
Δ = b2-4ac
Δ = 492-4·28·(-105)
Δ = 14161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14161}=119$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(49)-119}{2*28}=\frac{-168}{56}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(49)+119}{2*28}=\frac{70}{56}
=1+1/4
$