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7x-3(4x-8)6x=12-9x
We move all terms to the left:
7x-3(4x-8)6x-(12-9x)=0
We add all the numbers together, and all the variables
7x-3(4x-8)6x-(-9x+12)=0
We multiply parentheses
-72x^2+7x+144x-(-9x+12)=0
We get rid of parentheses
-72x^2+7x+144x+9x-12=0
We add all the numbers together, and all the variables
-72x^2+160x-12=0
a = -72; b = 160; c = -12;
Δ = b2-4ac
Δ = 1602-4·(-72)·(-12)
Δ = 22144
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{22144}=\sqrt{64*346}=\sqrt{64}*\sqrt{346}=8\sqrt{346}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-8\sqrt{346}}{2*-72}=\frac{-160-8\sqrt{346}}{-144} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+8\sqrt{346}}{2*-72}=\frac{-160+8\sqrt{346}}{-144} $
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