(X-2)(4x-5)=0

Solution for (X-2)(4x-5)=0 equation:

(X-2)(4X-5)=0

We multiply parentheses ..

(+4X^2-5X-8X+10)=0

We get rid of parentheses

4X^2-5X-8X+10=0

We add all the numbers together, and all the variables

4X^2-13X+10=0

a = 4; b = -13; c = +10;
Δ = b2-4ac
Δ = -132-4·4·10
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{-(-13)-3}{2*4}=\frac{10}{8}
=1+1/4
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+3}{2*4}=\frac{16}{8}
=2
$