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-6x^2+10x=-44
We move all terms to the left:
-6x^2+10x-(-44)=0
We add all the numbers together, and all the variables
-6x^2+10x+44=0
a = -6; b = 10; c = +44;
Δ = b2-4ac
Δ = 102-4·(-6)·44
Δ = 1156
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{1156}=34$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-34}{2*-6}=\frac{-44}{-12} =3+2/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+34}{2*-6}=\frac{24}{-12} =-2 $
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