-6/5x+25=9/2x-89

Solution for -6/5x+25=9/2x-89 equation:

-6/5x+25=9/2x-89

We move all terms to the left:

-6/5x+25-(9/2x-89)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x-89)!=0

x∈R


We get rid of parentheses

-6/5x-9/2x+89+25=0

We calculate fractions


(-12x)/10x^2+(-45x)/10x^2+89+25=0

We add all the numbers together, and all the variables

(-12x)/10x^2+(-45x)/10x^2+114=0

We multiply all the terms by the denominator


(-12x)+(-45x)+114*10x^2=0

Wy multiply elements

1140x^2+(-12x)+(-45x)=0

We get rid of parentheses

1140x^2-12x-45x=0

We add all the numbers together, and all the variables

1140x^2-57x=0

a = 1140; b = -57; c = 0;
Δ = b2-4ac
Δ = -572-4·1140·0
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-57)-57}{2*1140}=\frac{0}{2280}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-57)+57}{2*1140}=\frac{114}{2280}
=1/20
$