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24x+12=2(12x+6)12x+21=3(4x+6)
We move all terms to the left:
24x+12-(2(12x+6)12x+21)=0
We calculate terms in parentheses: -(2(12x+6)12x+21), so:We get rid of parentheses
2(12x+6)12x+21
We multiply parentheses
288x^2+144x+21
Back to the equation:
-(288x^2+144x+21)
-288x^2+24x-144x-21+12=0
We add all the numbers together, and all the variables
-288x^2-120x-9=0
a = -288; b = -120; c = -9;
Δ = b2-4ac
Δ = -1202-4·(-288)·(-9)
Δ = 4032
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4032}=\sqrt{576*7}=\sqrt{576}*\sqrt{7}=24\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-24\sqrt{7}}{2*-288}=\frac{120-24\sqrt{7}}{-576} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+24\sqrt{7}}{2*-288}=\frac{120+24\sqrt{7}}{-576} $
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