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-5x^2+6x=-8
We move all terms to the left:
-5x^2+6x-(-8)=0
We add all the numbers together, and all the variables
-5x^2+6x+8=0
a = -5; b = 6; c = +8;
Δ = b2-4ac
Δ = 62-4·(-5)·8
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-14}{2*-5}=\frac{-20}{-10} =+2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+14}{2*-5}=\frac{8}{-10} =-4/5 $
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