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2x^2=13x-7
We move all terms to the left:
2x^2-(13x-7)=0
We get rid of parentheses
2x^2-13x+7=0
a = 2; b = -13; c = +7;
Δ = b2-4ac
Δ = -132-4·2·7
Δ = 113
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{-(-13)-\sqrt{113}}{2*2}=\frac{13-\sqrt{113}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{113}}{2*2}=\frac{13+\sqrt{113}}{4} $
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