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-2x^2+6x-4=-24
We move all terms to the left:
-2x^2+6x-4-(-24)=0
We add all the numbers together, and all the variables
-2x^2+6x+20=0
a = -2; b = 6; c = +20;
Δ = b2-4ac
Δ = 62-4·(-2)·20
Δ = 196
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{196}=14$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-14}{2*-2}=\frac{-20}{-4} =+5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+14}{2*-2}=\frac{8}{-4} =-2 $
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