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X=(2X-7)(3X-1)=(2X-5)(3X+5)
We move all terms to the left:
X-((2X-7)(3X-1))=0
We multiply parentheses ..
-((+6X^2-2X-21X+7))+X=0
We calculate terms in parentheses: -((+6X^2-2X-21X+7)), so:We add all the numbers together, and all the variables
(+6X^2-2X-21X+7)
We get rid of parentheses
6X^2-2X-21X+7
We add all the numbers together, and all the variables
6X^2-23X+7
Back to the equation:
-(6X^2-23X+7)
X-(6X^2-23X+7)=0
We get rid of parentheses
-6X^2+X+23X-7=0
We add all the numbers together, and all the variables
-6X^2+24X-7=0
a = -6; b = 24; c = -7;
Δ = b2-4ac
Δ = 242-4·(-6)·(-7)
Δ = 408
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{408}=\sqrt{4*102}=\sqrt{4}*\sqrt{102}=2\sqrt{102}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{102}}{2*-6}=\frac{-24-2\sqrt{102}}{-12} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{102}}{2*-6}=\frac{-24+2\sqrt{102}}{-12} $
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