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5x^2-6-10x^2+8+4x=0
We add all the numbers together, and all the variables
-5x^2+4x+2=0
a = -5; b = 4; c = +2;
Δ = b2-4ac
Δ = 42-4·(-5)·2
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{-(4)-2\sqrt{14}}{2*-5}=\frac{-4-2\sqrt{14}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{14}}{2*-5}=\frac{-4+2\sqrt{14}}{-10} $
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