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-19+8x=-4x^2+2x
We move all terms to the left:
-19+8x-(-4x^2+2x)=0
We get rid of parentheses
4x^2-2x+8x-19=0
We add all the numbers together, and all the variables
4x^2+6x-19=0
a = 4; b = 6; c = -19;
Δ = b2-4ac
Δ = 62-4·4·(-19)
Δ = 340
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{85}}{2*4}=\frac{-6-2\sqrt{85}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{85}}{2*4}=\frac{-6+2\sqrt{85}}{8} $
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