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2x(8x-2)=12x+24
We move all terms to the left:
2x(8x-2)-(12x+24)=0
We multiply parentheses
16x^2-4x-(12x+24)=0
We get rid of parentheses
16x^2-4x-12x-24=0
We add all the numbers together, and all the variables
16x^2-16x-24=0
a = 16; b = -16; c = -24;
Δ = b2-4ac
Δ = -162-4·16·(-24)
Δ = 1792
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1792}=\sqrt{256*7}=\sqrt{256}*\sqrt{7}=16\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16\sqrt{7}}{2*16}=\frac{16-16\sqrt{7}}{32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16\sqrt{7}}{2*16}=\frac{16+16\sqrt{7}}{32} $
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