(2x-1)(x-2)=63

Solution for (2x-1)(x-2)=63 equation:

(2x-1)(x-2)=63

We move all terms to the left:

(2x-1)(x-2)-(63)=0

We multiply parentheses ..

(+2x^2-4x-1x+2)-63=0

We get rid of parentheses

2x^2-4x-1x+2-63=0

We add all the numbers together, and all the variables

2x^2-5x-61=0

a = 2; b = -5; c = -61;
Δ = b2-4ac
Δ = -52-4·2·(-61)
Δ = 513
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{513}=\sqrt{9*57}=\sqrt{9}*\sqrt{57}=3\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3\sqrt{57}}{2*2}=\frac{5-3\sqrt{57}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3\sqrt{57}}{2*2}=\frac{5+3\sqrt{57}}{4}
$