(2x-5)(x-+1)=12x

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Solution for (2x-5)(x-+1)=12x equation:



(2x-5)(x-+1)=12x
We move all terms to the left:
(2x-5)(x-+1)-(12x)=0
We add all the numbers together, and all the variables
(2x-5)(+x)-12x=0
We add all the numbers together, and all the variables
-12x+(2x-5)(+x)=0
We multiply parentheses ..
(+2x^2-5x)-12x=0
We get rid of parentheses
2x^2-5x-12x=0
We add all the numbers together, and all the variables
2x^2-17x=0
a = 2; b = -17; c = 0;
Δ = b2-4ac
Δ = -172-4·2·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-17}{2*2}=\frac{0}{4} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+17}{2*2}=\frac{34}{4} =8+1/2 $

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