(4x-7)(6x-13)=0

Solution for (4x-7)(6x-13)=0 equation:

(4x-7)(6x-13)=0

We multiply parentheses ..

(+24x^2-52x-42x+91)=0

We get rid of parentheses

24x^2-52x-42x+91=0

We add all the numbers together, and all the variables

24x^2-94x+91=0

a = 24; b = -94; c = +91;
Δ = b2-4ac
Δ = -942-4·24·91
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-94)-10}{2*24}=\frac{84}{48}
=1+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-94)+10}{2*24}=\frac{104}{48}
=2+1/6
$