(x-2)(2x-5)=10

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Solution for (x-2)(2x-5)=10 equation:



(x-2)(2x-5)=10
We move all terms to the left:
(x-2)(2x-5)-(10)=0
We multiply parentheses ..
(+2x^2-5x-4x+10)-10=0
We get rid of parentheses
2x^2-5x-4x+10-10=0
We add all the numbers together, and all the variables
2x^2-9x=0
a = 2; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·2·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*2}=\frac{0}{4} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*2}=\frac{18}{4} =4+1/2 $

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