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4x^2-(2-5x^2)=0.5x^2
We move all terms to the left:
4x^2-(2-5x^2)-(0.5x^2)=0
We get rid of parentheses
4x^2+5x^2-0.5x^2-2=0
We add all the numbers together, and all the variables
8.5x^2-2=0
a = 8.5; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·8.5·(-2)
Δ = 68
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{17}}{2*8.5}=\frac{0-2\sqrt{17}}{17} =-\frac{2\sqrt{17}}{17} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{17}}{2*8.5}=\frac{0+2\sqrt{17}}{17} =\frac{2\sqrt{17}}{17} $
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