300=(2x-9)(x-5)

Solution for 300=(2x-9)(x-5) equation:

300=(2x-9)(x-5)

We move all terms to the left:

300-((2x-9)(x-5))=0

We multiply parentheses ..

-((+2x^2-10x-9x+45))+300=0


We calculate terms in parentheses: -((+2x^2-10x-9x+45)), so:

(+2x^2-10x-9x+45)

We get rid of parentheses

2x^2-10x-9x+45

We add all the numbers together, and all the variables

2x^2-19x+45

Back to the equation:

-(2x^2-19x+45)


We get rid of parentheses

-2x^2+19x-45+300=0

We add all the numbers together, and all the variables

-2x^2+19x+255=0

a = -2; b = 19; c = +255;
Δ = b2-4ac
Δ = 192-4·(-2)·255
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-49}{2*-2}=\frac{-68}{-4}
=+17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+49}{2*-2}=\frac{30}{-4}
=-7+1/2
$