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5x^2-16+4x^2-6x=180
We move all terms to the left:
5x^2-16+4x^2-6x-(180)=0
We add all the numbers together, and all the variables
9x^2-6x-196=0
a = 9; b = -6; c = -196;
Δ = b2-4ac
Δ = -62-4·9·(-196)
Δ = 7092
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7092}=\sqrt{36*197}=\sqrt{36}*\sqrt{197}=6\sqrt{197}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{197}}{2*9}=\frac{6-6\sqrt{197}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{197}}{2*9}=\frac{6+6\sqrt{197}}{18} $
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