(2x-24)+(x2)=180

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Solution for (2x-24)+(x2)=180 equation:



(2x-24)+(x2)=180
We move all terms to the left:
(2x-24)+(x2)-(180)=0
We add all the numbers together, and all the variables
x^2+(2x-24)-180=0
We get rid of parentheses
x^2+2x-24-180=0
We add all the numbers together, and all the variables
x^2+2x-204=0
a = 1; b = 2; c = -204;
Δ = b2-4ac
Δ = 22-4·1·(-204)
Δ = 820
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{820}=\sqrt{4*205}=\sqrt{4}*\sqrt{205}=2\sqrt{205}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{205}}{2*1}=\frac{-2-2\sqrt{205}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{205}}{2*1}=\frac{-2+2\sqrt{205}}{2} $

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