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

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

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

We multiply parentheses ..

(+5x^2-5x-6x+6)=0

We get rid of parentheses

5x^2-5x-6x+6=0

We add all the numbers together, and all the variables

5x^2-11x+6=0

a = 5; b = -11; c = +6;
Δ = b2-4ac
Δ = -112-4·5·6
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-1}{2*5}=\frac{10}{10}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+1}{2*5}=\frac{12}{10}
=1+1/5
$