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x=-6x^2+8x+4
We move all terms to the left:
x-(-6x^2+8x+4)=0
We get rid of parentheses
6x^2-8x+x-4=0
We add all the numbers together, and all the variables
6x^2-7x-4=0
a = 6; b = -7; c = -4;
Δ = b2-4ac
Δ = -72-4·6·(-4)
Δ = 145
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{145}}{2*6}=\frac{7-\sqrt{145}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{145}}{2*6}=\frac{7+\sqrt{145}}{12} $
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