(2x+1)(4x-21)=0

Solution for (2x+1)(4x-21)=0 equation:

(2x+1)(4x-21)=0

We multiply parentheses ..

(+8x^2-42x+4x-21)=0

We get rid of parentheses

8x^2-42x+4x-21=0

We add all the numbers together, and all the variables

8x^2-38x-21=0

a = 8; b = -38; c = -21;
Δ = b2-4ac
Δ = -382-4·8·(-21)
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-46}{2*8}=\frac{-8}{16}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+46}{2*8}=\frac{84}{16}
=5+1/4
$