2x(x+69)=180

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Solution for 2x(x+69)=180 equation:



2x(x+69)=180
We move all terms to the left:
2x(x+69)-(180)=0
We multiply parentheses
2x^2+138x-180=0
a = 2; b = 138; c = -180;
Δ = b2-4ac
Δ = 1382-4·2·(-180)
Δ = 20484
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:
$\sqrt{\Delta}=\sqrt{20484}=\sqrt{36*569}=\sqrt{36}*\sqrt{569}=6\sqrt{569}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(138)-6\sqrt{569}}{2*2}=\frac{-138-6\sqrt{569}}{4} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(138)+6\sqrt{569}}{2*2}=\frac{-138+6\sqrt{569}}{4} $

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