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4x+2x(x-1)=10
We move all terms to the left:
4x+2x(x-1)-(10)=0
We multiply parentheses
2x^2+4x-2x-10=0
We add all the numbers together, and all the variables
2x^2+2x-10=0
a = 2; b = 2; c = -10;
Δ = b2-4ac
Δ = 22-4·2·(-10)
Δ = 84
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{21}}{2*2}=\frac{-2-2\sqrt{21}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{21}}{2*2}=\frac{-2+2\sqrt{21}}{4} $
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