7/6x=x+25

Solution for 7/6x=x+25 equation:

7/6x=x+25

We move all terms to the left:

7/6x-(x+25)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

7/6x-x-25=0

We multiply all the terms by the denominator


-x*6x-25*6x+7=0

Wy multiply elements

-6x^2-150x+7=0

a = -6; b = -150; c = +7;
Δ = b2-4ac
Δ = -1502-4·(-6)·7
Δ = 22668
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:

$\sqrt{\Delta}=\sqrt{22668}=\sqrt{4*5667}=\sqrt{4}*\sqrt{5667}=2\sqrt{5667}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-2\sqrt{5667}}{2*-6}=\frac{150-2\sqrt{5667}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+2\sqrt{5667}}{2*-6}=\frac{150+2\sqrt{5667}}{-12}
$