x^2+23x-138x=8x-4x^2+2

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Solution for x^2+23x-138x=8x-4x^2+2 equation:



x^2+23x-138x=8x-4x^2+2
We move all terms to the left:
x^2+23x-138x-(8x-4x^2+2)=0
We add all the numbers together, and all the variables
x^2-(8x-4x^2+2)-115x=0
We get rid of parentheses
x^2+4x^2-8x-115x-2=0
We add all the numbers together, and all the variables
5x^2-123x-2=0
a = 5; b = -123; c = -2;
Δ = b2-4ac
Δ = -1232-4·5·(-2)
Δ = 15169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-123)-\sqrt{15169}}{2*5}=\frac{123-\sqrt{15169}}{10} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-123)+\sqrt{15169}}{2*5}=\frac{123+\sqrt{15169}}{10} $

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