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5x^2-6x+4=12
We move all terms to the left:
5x^2-6x+4-(12)=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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-14}{2*5}=\frac{-8}{10} =-4/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+14}{2*5}=\frac{20}{10} =2 $
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