-2/3x=x+25

Solution for -2/3x=x+25 equation:

-2/3x=x+25

We move all terms to the left:

-2/3x-(x+25)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

-2/3x-x-25=0

We multiply all the terms by the denominator


-x*3x-25*3x-2=0

Wy multiply elements

-3x^2-75x-2=0

a = -3; b = -75; c = -2;
Δ = b2-4ac
Δ = -752-4·(-3)·(-2)
Δ = 5601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-\sqrt{5601}}{2*-3}=\frac{75-\sqrt{5601}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+\sqrt{5601}}{2*-3}=\frac{75+\sqrt{5601}}{-6}
$