(2x-3)(x-2)=21

Solution for (2x-3)(x-2)=21 equation:

(2x-3)(x-2)=21

We move all terms to the left:

(2x-3)(x-2)-(21)=0

We multiply parentheses ..

(+2x^2-4x-3x+6)-21=0

We get rid of parentheses

2x^2-4x-3x+6-21=0

We add all the numbers together, and all the variables

2x^2-7x-15=0

a = 2; b = -7; c = -15;
Δ = b2-4ac
Δ = -72-4·2·(-15)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-13}{2*2}=\frac{-6}{4}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+13}{2*2}=\frac{20}{4}
=5
$