x+2=22-7/8x-15

Solution for x+2=22-7/8x-15 equation:

x+2=22-7/8x-15

We move all terms to the left:

x+2-(22-7/8x-15)=0


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

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

x+7/8x-7+2=0

We multiply all the terms by the denominator


x*8x-7*8x+2*8x+7=0

Wy multiply elements

8x^2-56x+16x+7=0

We add all the numbers together, and all the variables

8x^2-40x+7=0

a = 8; b = -40; c = +7;
Δ = b2-4ac
Δ = -402-4·8·7
Δ = 1376
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:

$\sqrt{\Delta}=\sqrt{1376}=\sqrt{16*86}=\sqrt{16}*\sqrt{86}=4\sqrt{86}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{86}}{2*8}=\frac{40-4\sqrt{86}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{86}}{2*8}=\frac{40+4\sqrt{86}}{16}
$