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-3x^2+2x=-7
We move all terms to the left:
-3x^2+2x-(-7)=0
We add all the numbers together, and all the variables
-3x^2+2x+7=0
a = -3; b = 2; c = +7;
Δ = b2-4ac
Δ = 22-4·(-3)·7
Δ = 88
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{22}}{2*-3}=\frac{-2-2\sqrt{22}}{-6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{22}}{2*-3}=\frac{-2+2\sqrt{22}}{-6} $
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