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2x^2-7x=32
We move all terms to the left:
2x^2-7x-(32)=0
a = 2; b = -7; c = -32;
Δ = b2-4ac
Δ = -72-4·2·(-32)
Δ = 305
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{305}}{2*2}=\frac{7-\sqrt{305}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{305}}{2*2}=\frac{7+\sqrt{305}}{4} $
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