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5x^2-2-4x=6
We move all terms to the left:
5x^2-2-4x-(6)=0
We add all the numbers together, and all the variables
5x^2-4x-8=0
a = 5; b = -4; c = -8;
Δ = b2-4ac
Δ = -42-4·5·(-8)
Δ = 176
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{11}}{2*5}=\frac{4-4\sqrt{11}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{11}}{2*5}=\frac{4+4\sqrt{11}}{10} $
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