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2x+2x(3x+1)=90
We move all terms to the left:
2x+2x(3x+1)-(90)=0
We multiply parentheses
6x^2+2x+2x-90=0
We add all the numbers together, and all the variables
6x^2+4x-90=0
a = 6; b = 4; c = -90;
Δ = b2-4ac
Δ = 42-4·6·(-90)
Δ = 2176
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2176}=\sqrt{64*34}=\sqrt{64}*\sqrt{34}=8\sqrt{34}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8\sqrt{34}}{2*6}=\frac{-4-8\sqrt{34}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8\sqrt{34}}{2*6}=\frac{-4+8\sqrt{34}}{12} $
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