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189=-6x(-7x-18)
We move all terms to the left:
189-(-6x(-7x-18))=0
We calculate terms in parentheses: -(-6x(-7x-18)), so:We get rid of parentheses
-6x(-7x-18)
We multiply parentheses
42x^2+108x
Back to the equation:
-(42x^2+108x)
-42x^2-108x+189=0
a = -42; b = -108; c = +189;
Δ = b2-4ac
Δ = -1082-4·(-42)·189
Δ = 43416
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{43416}=\sqrt{324*134}=\sqrt{324}*\sqrt{134}=18\sqrt{134}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-18\sqrt{134}}{2*-42}=\frac{108-18\sqrt{134}}{-84} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+18\sqrt{134}}{2*-42}=\frac{108+18\sqrt{134}}{-84} $
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