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X(6X+1)-12X=5
We move all terms to the left:
X(6X+1)-12X-(5)=0
We add all the numbers together, and all the variables
-12X+X(6X+1)-5=0
We multiply parentheses
6X^2-12X+X-5=0
We add all the numbers together, and all the variables
6X^2-11X-5=0
a = 6; b = -11; c = -5;
Δ = b2-4ac
Δ = -112-4·6·(-5)
Δ = 241
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{-(-11)-\sqrt{241}}{2*6}=\frac{11-\sqrt{241}}{12} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{241}}{2*6}=\frac{11+\sqrt{241}}{12} $
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