x2+x+(x+84)=180

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Solution for x2+x+(x+84)=180 equation:



x2+x+(x+84)=180
We move all terms to the left:
x2+x+(x+84)-(180)=0
We add all the numbers together, and all the variables
x^2+x+(x+84)-180=0
We get rid of parentheses
x^2+x+x+84-180=0
We add all the numbers together, and all the variables
x^2+2x-96=0
a = 1; b = 2; c = -96;
Δ = b2-4ac
Δ = 22-4·1·(-96)
Δ = 388
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:
$\sqrt{\Delta}=\sqrt{388}=\sqrt{4*97}=\sqrt{4}*\sqrt{97}=2\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{97}}{2*1}=\frac{-2-2\sqrt{97}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{97}}{2*1}=\frac{-2+2\sqrt{97}}{2} $

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