(2x-3)(-x+36)=103

Solution for (2x-3)(-x+36)=103 equation:

(2x-3)(-x+36)=103

We move all terms to the left:

(2x-3)(-x+36)-(103)=0

We add all the numbers together, and all the variables

(2x-3)(-1x+36)-103=0

We multiply parentheses ..

(-2x^2+72x+3x-108)-103=0

We get rid of parentheses

-2x^2+72x+3x-108-103=0

We add all the numbers together, and all the variables

-2x^2+75x-211=0

a = -2; b = 75; c = -211;
Δ = b2-4ac
Δ = 752-4·(-2)·(-211)
Δ = 3937
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{-(75)-\sqrt{3937}}{2*-2}=\frac{-75-\sqrt{3937}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+\sqrt{3937}}{2*-2}=\frac{-75+\sqrt{3937}}{-4}
$