2+x=7/8x-15

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

2+x=7/8x-15

We move all terms to the left:

2+x-(7/8x-15)=0


Domain of the equation: 8x-15)!=0

x∈R


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}
$