(-7x+9)(6x-1)=0

Solution for (-7x+9)(6x-1)=0 equation:

(-7x+9)(6x-1)=0

We multiply parentheses ..

(-42x^2+7x+54x-9)=0

We get rid of parentheses

-42x^2+7x+54x-9=0

We add all the numbers together, and all the variables

-42x^2+61x-9=0

a = -42; b = 61; c = -9;
Δ = b2-4ac
Δ = 612-4·(-42)·(-9)
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(61)-47}{2*-42}=\frac{-108}{-84}
=1+2/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(61)+47}{2*-42}=\frac{-14}{-84}
=1/6
$