X-25=1/3x+121

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Solution for X-25=1/3x+121 equation:



X-25=1/3X+121
We move all terms to the left:
X-25-(1/3X+121)=0
Domain of the equation: 3X+121)!=0
X∈R
We get rid of parentheses
X-1/3X-121-25=0
We multiply all the terms by the denominator
X*3X-121*3X-25*3X-1=0
Wy multiply elements
3X^2-363X-75X-1=0
We add all the numbers together, and all the variables
3X^2-438X-1=0
a = 3; b = -438; c = -1;
Δ = b2-4ac
Δ = -4382-4·3·(-1)
Δ = 191856
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:
$\sqrt{\Delta}=\sqrt{191856}=\sqrt{16*11991}=\sqrt{16}*\sqrt{11991}=4\sqrt{11991}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-438)-4\sqrt{11991}}{2*3}=\frac{438-4\sqrt{11991}}{6} $
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-438)+4\sqrt{11991}}{2*3}=\frac{438+4\sqrt{11991}}{6} $

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