(x-42)(x-45)=75

Solution for (x-42)(x-45)=75 equation:

(x-42)(x-45)=75

We move all terms to the left:

(x-42)(x-45)-(75)=0

We multiply parentheses ..

(+x^2-45x-42x+1890)-75=0

We get rid of parentheses

x^2-45x-42x+1890-75=0

We add all the numbers together, and all the variables

x^2-87x+1815=0

a = 1; b = -87; c = +1815;
Δ = b2-4ac
Δ = -872-4·1·1815
Δ = 309
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-87)-\sqrt{309}}{2*1}=\frac{87-\sqrt{309}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-87)+\sqrt{309}}{2*1}=\frac{87+\sqrt{309}}{2}
$