(-9)/(2)x=-9-5x

Solution for (-9)/(2)x=-9-5x equation:

(-9)/(2)x=-9-5x

We move all terms to the left:

(-9)/(2)x-(-9-5x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

(-9)/2x-(-5x-9)=0

We get rid of parentheses

(-9)/2x+5x+9=0

We multiply all the terms by the denominator


5x*2x+9*2x+(-9)=0

We add all the numbers together, and all the variables

5x*2x+9*2x-9=0

Wy multiply elements

10x^2+18x-9=0

a = 10; b = 18; c = -9;
Δ = b2-4ac
Δ = 182-4·10·(-9)
Δ = 684
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:

$\sqrt{\Delta}=\sqrt{684}=\sqrt{36*19}=\sqrt{36}*\sqrt{19}=6\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{19}}{2*10}=\frac{-18-6\sqrt{19}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{19}}{2*10}=\frac{-18+6\sqrt{19}}{20}
$