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X(2X+1)=74
We move all terms to the left:
X(2X+1)-(74)=0
We multiply parentheses
2X^2+X-74=0
a = 2; b = 1; c = -74;
Δ = b2-4ac
Δ = 12-4·2·(-74)
Δ = 593
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{593}}{2*2}=\frac{-1-\sqrt{593}}{4} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{593}}{2*2}=\frac{-1+\sqrt{593}}{4} $
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