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X(2X-11)=14
We move all terms to the left:
X(2X-11)-(14)=0
We multiply parentheses
2X^2-11X-14=0
a = 2; b = -11; c = -14;
Δ = b2-4ac
Δ = -112-4·2·(-14)
Δ = 233
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{233}}{2*2}=\frac{11-\sqrt{233}}{4} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{233}}{2*2}=\frac{11+\sqrt{233}}{4} $
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