(X-4)(2x-19)=36(x+3)

Solution for (X-4)(2x-19)=36(x+3) equation:

(X-4)(2X-19)=36(X+3)

We move all terms to the left:

(X-4)(2X-19)-(36(X+3))=0

We multiply parentheses ..

(+2X^2-19X-8X+76)-(36(X+3))=0


We calculate terms in parentheses: -(36(X+3)), so:

36(X+3)

We multiply parentheses

36X+108

Back to the equation:

-(36X+108)


We get rid of parentheses

2X^2-19X-8X-36X+76-108=0

We add all the numbers together, and all the variables

2X^2-63X-32=0

a = 2; b = -63; c = -32;
Δ = b2-4ac
Δ = -632-4·2·(-32)
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-65}{2*2}=\frac{-2}{4}
=-1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+65}{2*2}=\frac{128}{4}
=32
$