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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

28x^2-31x+6=0

a = 28; b = -31; c = +6;
Δ = b2-4ac
Δ = -312-4·28·6
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-17}{2*28}=\frac{14}{56}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+17}{2*28}=\frac{48}{56}
=6/7
$