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-4x(2x-6)=12x-6
We move all terms to the left:
-4x(2x-6)-(12x-6)=0
We multiply parentheses
-8x^2+24x-(12x-6)=0
We get rid of parentheses
-8x^2+24x-12x+6=0
We add all the numbers together, and all the variables
-8x^2+12x+6=0
a = -8; b = 12; c = +6;
Δ = b2-4ac
Δ = 122-4·(-8)·6
Δ = 336
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{21}}{2*-8}=\frac{-12-4\sqrt{21}}{-16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{21}}{2*-8}=\frac{-12+4\sqrt{21}}{-16} $
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