-7+x=1/10x-16

Solution for -7+x=1/10x-16 equation:

-7+x=1/10x-16

We move all terms to the left:

-7+x-(1/10x-16)=0


Domain of the equation: 10x-16)!=0

x∈R


We get rid of parentheses

x-1/10x+16-7=0

We multiply all the terms by the denominator


x*10x+16*10x-7*10x-1=0

Wy multiply elements

10x^2+160x-70x-1=0

We add all the numbers together, and all the variables

10x^2+90x-1=0

a = 10; b = 90; c = -1;
Δ = b2-4ac
Δ = 902-4·10·(-1)
Δ = 8140
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:

$\sqrt{\Delta}=\sqrt{8140}=\sqrt{4*2035}=\sqrt{4}*\sqrt{2035}=2\sqrt{2035}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-2\sqrt{2035}}{2*10}=\frac{-90-2\sqrt{2035}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+2\sqrt{2035}}{2*10}=\frac{-90+2\sqrt{2035}}{20}
$