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-7x(-6x+3)=189
We move all terms to the left:
-7x(-6x+3)-(189)=0
We multiply parentheses
42x^2-21x-189=0
a = 42; b = -21; c = -189;
Δ = b2-4ac
Δ = -212-4·42·(-189)
Δ = 32193
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{32193}=\sqrt{441*73}=\sqrt{441}*\sqrt{73}=21\sqrt{73}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21\sqrt{73}}{2*42}=\frac{21-21\sqrt{73}}{84} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21\sqrt{73}}{2*42}=\frac{21+21\sqrt{73}}{84} $
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