(2x+17)/(x+7)=x+5

Solution for (2x+17)/(x+7)=x+5 equation:

(2x+17)/(x+7)=x+5

We move all terms to the left:

(2x+17)/(x+7)-(x+5)=0


Domain of the equation: (x+7)!=0

We move all terms containing x to the left, all other terms to the right

x!=-7

x∈R


We get rid of parentheses

(2x+17)/(x+7)-x-5=0

We multiply all the terms by the denominator


(2x+17)-x*(x+7)-5*(x+7)=0

We multiply parentheses

-x^2+(2x+17)-7x-5x-35=0

We get rid of parentheses

-x^2+2x-7x-5x+17-35=0

We add all the numbers together, and all the variables

-1x^2-10x-18=0

a = -1; b = -10; c = -18;
Δ = b2-4ac
Δ = -102-4·(-1)·(-18)
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{7}}{2*-1}=\frac{10-2\sqrt{7}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{7}}{2*-1}=\frac{10+2\sqrt{7}}{-2}
$