x2-12(8-x)=6x+3(6-4x)-1

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Solution for x2-12(8-x)=6x+3(6-4x)-1 equation:



x2-12(8-x)=6x+3(6-4x)-1
We move all terms to the left:
x2-12(8-x)-(6x+3(6-4x)-1)=0
We add all the numbers together, and all the variables
x2-12(-1x+8)-(6x+3(-4x+6)-1)=0
We add all the numbers together, and all the variables
x^2-12(-1x+8)-(6x+3(-4x+6)-1)=0
We multiply parentheses
x^2+12x-(6x+3(-4x+6)-1)-96=0
We calculate terms in parentheses: -(6x+3(-4x+6)-1), so:
6x+3(-4x+6)-1
We multiply parentheses
6x-12x+18-1
We add all the numbers together, and all the variables
-6x+17
Back to the equation:
-(-6x+17)
We get rid of parentheses
x^2+12x+6x-17-96=0
We add all the numbers together, and all the variables
x^2+18x-113=0
a = 1; b = 18; c = -113;
Δ = b2-4ac
Δ = 182-4·1·(-113)
Δ = 776
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:
$\sqrt{\Delta}=\sqrt{776}=\sqrt{4*194}=\sqrt{4}*\sqrt{194}=2\sqrt{194}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{194}}{2*1}=\frac{-18-2\sqrt{194}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{194}}{2*1}=\frac{-18+2\sqrt{194}}{2} $

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