(4x+1)(6x-7)=0

Solution for (4x+1)(6x-7)=0 equation:

(4x+1)(6x-7)=0

We multiply parentheses ..

(+24x^2-28x+6x-7)=0

We get rid of parentheses

24x^2-28x+6x-7=0

We add all the numbers together, and all the variables

24x^2-22x-7=0

a = 24; b = -22; c = -7;
Δ = b2-4ac
Δ = -222-4·24·(-7)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-34}{2*24}=\frac{-12}{48}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+34}{2*24}=\frac{56}{48}
=1+1/6
$