2+x=-15+7/8x

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Solution for 2+x=-15+7/8x equation:



2+x=-15+7/8x
We move all terms to the left:
2+x-(-15+7/8x)=0
Domain of the equation: 8x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
x-(7/8x-15)+2=0
We get rid of parentheses
x-7/8x+15+2=0
We multiply all the terms by the denominator
x*8x+15*8x+2*8x-7=0
Wy multiply elements
8x^2+120x+16x-7=0
We add all the numbers together, and all the variables
8x^2+136x-7=0
a = 8; b = 136; c = -7;
Δ = b2-4ac
Δ = 1362-4·8·(-7)
Δ = 18720
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:
$\sqrt{\Delta}=\sqrt{18720}=\sqrt{144*130}=\sqrt{144}*\sqrt{130}=12\sqrt{130}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(136)-12\sqrt{130}}{2*8}=\frac{-136-12\sqrt{130}}{16} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(136)+12\sqrt{130}}{2*8}=\frac{-136+12\sqrt{130}}{16} $

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