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

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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 $

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