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-2x^2+5x+14=7
We move all terms to the left:
-2x^2+5x+14-(7)=0
We add all the numbers together, and all the variables
-2x^2+5x+7=0
a = -2; b = 5; c = +7;
Δ = b2-4ac
Δ = 52-4·(-2)·7
Δ = 81
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{81}=9$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-9}{2*-2}=\frac{-14}{-4} =3+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+9}{2*-2}=\frac{4}{-4} =-1 $
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