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2.5-2x2=6x

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Solution for 2.5-2x2=6x equation:



2.5-2x^2=6x
We move all terms to the left:
2.5-2x^2-(6x)=0
a = -2; b = -6; c = +2.5;
Δ = b2-4ac
Δ = -62-4·(-2)·2.5
Δ = 56
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{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}
x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{14}}{2*-2}=\frac{6-2\sqrt{14}}{-4}
x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{14}}{2*-2}=\frac{6+2\sqrt{14}}{-4}

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