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-24+12-10=-4x(-3x+8)-2
We move all terms to the left:
-24+12-10-(-4x(-3x+8)-2)=0
We add all the numbers together, and all the variables
-(-4x(-3x+8)-2)-22=0
We calculate terms in parentheses: -(-4x(-3x+8)-2), so:We get rid of parentheses
-4x(-3x+8)-2
We multiply parentheses
12x^2-32x-2
Back to the equation:
-(12x^2-32x-2)
-12x^2+32x+2-22=0
We add all the numbers together, and all the variables
-12x^2+32x-20=0
a = -12; b = 32; c = -20;
Δ = b2-4ac
Δ = 322-4·(-12)·(-20)
Δ = 64
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{64}=8$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-8}{2*-12}=\frac{-40}{-24} =1+2/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+8}{2*-12}=\frac{-24}{-24} =1 $
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