2x(x-7)=18-x

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Solution for 2x(x-7)=18-x equation:



2x(x-7)=18-x
We move all terms to the left:
2x(x-7)-(18-x)=0
We add all the numbers together, and all the variables
2x(x-7)-(-1x+18)=0
We multiply parentheses
2x^2-14x-(-1x+18)=0
We get rid of parentheses
2x^2-14x+1x-18=0
We add all the numbers together, and all the variables
2x^2-13x-18=0
a = 2; b = -13; c = -18;
Δ = b2-4ac
Δ = -132-4·2·(-18)
Δ = 313
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{313}}{2*2}=\frac{13-\sqrt{313}}{4} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{313}}{2*2}=\frac{13+\sqrt{313}}{4} $

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