(X-5)(7x-8)=0

Solution for (X-5)(7x-8)=0 equation:

(X-5)(7X-8)=0

We multiply parentheses ..

(+7X^2-8X-35X+40)=0

We get rid of parentheses

7X^2-8X-35X+40=0

We add all the numbers together, and all the variables

7X^2-43X+40=0

a = 7; b = -43; c = +40;
Δ = b2-4ac
Δ = -432-4·7·40
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-43)-27}{2*7}=\frac{16}{14}
=1+1/7
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+27}{2*7}=\frac{70}{14}
=5
$