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X(7-5X)=6X-1
We move all terms to the left:
X(7-5X)-(6X-1)=0
We add all the numbers together, and all the variables
X(-5X+7)-(6X-1)=0
We multiply parentheses
-5X^2+7X-(6X-1)=0
We get rid of parentheses
-5X^2+7X-6X+1=0
We add all the numbers together, and all the variables
-5X^2+X+1=0
a = -5; b = 1; c = +1;
Δ = b2-4ac
Δ = 12-4·(-5)·1
Δ = 21
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{21}}{2*-5}=\frac{-1-\sqrt{21}}{-10} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{21}}{2*-5}=\frac{-1+\sqrt{21}}{-10} $
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