(4x+1)(2x-7)=0.

Solution for (4x+1)(2x-7)=0. equation:

(4x+1)(2x-7)=0.

We multiply parentheses ..

(+8x^2-28x+2x-7)=0

We get rid of parentheses

8x^2-28x+2x-7=0

We add all the numbers together, and all the variables

8x^2-26x-7=0

a = 8; b = -26; c = -7;
Δ = b2-4ac
Δ = -262-4·8·(-7)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-30}{2*8}=\frac{-4}{16}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+30}{2*8}=\frac{56}{16}
=3+1/2
$