(X-2)(2x-5)=6

Solution for (X-2)(2x-5)=6 equation:

(X-2)(2X-5)=6

We move all terms to the left:

(X-2)(2X-5)-(6)=0

We multiply parentheses ..

(+2X^2-5X-4X+10)-6=0

We get rid of parentheses

2X^2-5X-4X+10-6=0

We add all the numbers together, and all the variables

2X^2-9X+4=0

a = 2; b = -9; c = +4;
Δ = b2-4ac
Δ = -92-4·2·4
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-7}{2*2}=\frac{2}{4}
=1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+7}{2*2}=\frac{16}{4}
=4
$