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2x(3x-12)=4x-21
We move all terms to the left:
2x(3x-12)-(4x-21)=0
We multiply parentheses
6x^2-24x-(4x-21)=0
We get rid of parentheses
6x^2-24x-4x+21=0
We add all the numbers together, and all the variables
6x^2-28x+21=0
a = 6; b = -28; c = +21;
Δ = b2-4ac
Δ = -282-4·6·21
Δ = 280
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{70}}{2*6}=\frac{28-2\sqrt{70}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{70}}{2*6}=\frac{28+2\sqrt{70}}{12} $
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