(4x-5)(6x+1)=0

Solution for (4x-5)(6x+1)=0 equation:

(4x-5)(6x+1)=0

We multiply parentheses ..

(+24x^2+4x-30x-5)=0

We get rid of parentheses

24x^2+4x-30x-5=0

We add all the numbers together, and all the variables

24x^2-26x-5=0

a = 24; b = -26; c = -5;
Δ = b2-4ac
Δ = -262-4·24·(-5)
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{-(-26)-34}{2*24}=\frac{-8}{48}
=-1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+34}{2*24}=\frac{60}{48}
=1+1/4
$