(67+25)/(350+25x)=x

Solution for (67+25)/(350+25x)=x equation:

(67+25)/(350+25x)=x

We move all terms to the left:

(67+25)/(350+25x)-(x)=0


Domain of the equation: (350+25x)!=0

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

25x!=-350

x!=-350/25

x!=-14

x∈R


We add all the numbers together, and all the variables

92/(25x+350)-x=0

We add all the numbers together, and all the variables

-1x+92/(25x+350)=0

We multiply all the terms by the denominator


-1x*(25x+350)+92=0

We multiply parentheses

-25x^2-350x+92=0

a = -25; b = -350; c = +92;
Δ = b2-4ac
Δ = -3502-4·(-25)·92
Δ = 131700
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:

$\sqrt{\Delta}=\sqrt{131700}=\sqrt{100*1317}=\sqrt{100}*\sqrt{1317}=10\sqrt{1317}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-350)-10\sqrt{1317}}{2*-25}=\frac{350-10\sqrt{1317}}{-50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-350)+10\sqrt{1317}}{2*-25}=\frac{350+10\sqrt{1317}}{-50}
$