(-6x+7)(3x-4)=0

Solution for (-6x+7)(3x-4)=0 equation:

(-6x+7)(3x-4)=0

We multiply parentheses ..

(-18x^2+24x+21x-28)=0

We get rid of parentheses

-18x^2+24x+21x-28=0

We add all the numbers together, and all the variables

-18x^2+45x-28=0

a = -18; b = 45; c = -28;
Δ = b2-4ac
Δ = 452-4·(-18)·(-28)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-3}{2*-18}=\frac{-48}{-36}
=1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+3}{2*-18}=\frac{-42}{-36}
=1+1/6
$