9/10x+5=12+1/2x

Solution for 9/10x+5=12+1/2x equation:

9/10x+5=12+1/2x

We move all terms to the left:

9/10x+5-(12+1/2x)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

9/10x-(1/2x+12)+5=0

We get rid of parentheses

9/10x-1/2x-12+5=0

We calculate fractions


18x/20x^2+(-10x)/20x^2-12+5=0

We add all the numbers together, and all the variables

18x/20x^2+(-10x)/20x^2-7=0

We multiply all the terms by the denominator


18x+(-10x)-7*20x^2=0

Wy multiply elements

-140x^2+18x+(-10x)=0

We get rid of parentheses

-140x^2+18x-10x=0

We add all the numbers together, and all the variables

-140x^2+8x=0

a = -140; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-140)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-140}=\frac{-16}{-280}
=2/35
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-140}=\frac{0}{-280}
=0
$