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X(2X-7)=41
We move all terms to the left:
X(2X-7)-(41)=0
We multiply parentheses
2X^2-7X-41=0
a = 2; b = -7; c = -41;
Δ = b2-4ac
Δ = -72-4·2·(-41)
Δ = 377
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{-(-7)-\sqrt{377}}{2*2}=\frac{7-\sqrt{377}}{4} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{377}}{2*2}=\frac{7+\sqrt{377}}{4} $
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