(7x-6)(x-5)=0

Solution for (7x-6)(x-5)=0 equation:

(7x-6)(x-5)=0

We multiply parentheses ..

(+7x^2-35x-6x+30)=0

We get rid of parentheses

7x^2-35x-6x+30=0

We add all the numbers together, and all the variables

7x^2-41x+30=0

a = 7; b = -41; c = +30;
Δ = b2-4ac
Δ = -412-4·7·30
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41)-29}{2*7}=\frac{12}{14}
=6/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+29}{2*7}=\frac{70}{14}
=5
$