(2x-6)(-x+5)+x-3=0

Solution for (2x-6)(-x+5)+x-3=0 equation:

(2x-6)(-x+5)+x-3=0

We add all the numbers together, and all the variables

(2x-6)(-1x+5)+x-3=0

We add all the numbers together, and all the variables

x+(2x-6)(-1x+5)-3=0

We multiply parentheses ..

(-2x^2+10x+6x-30)+x-3=0

We get rid of parentheses

-2x^2+10x+6x+x-30-3=0

We add all the numbers together, and all the variables

-2x^2+17x-33=0

a = -2; b = 17; c = -33;
Δ = b2-4ac
Δ = 172-4·(-2)·(-33)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-5}{2*-2}=\frac{-22}{-4}
=5+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+5}{2*-2}=\frac{-12}{-4}
=+3
$