-1/5x+21=7/10x+12

Solution for -1/5x+21=7/10x+12 equation:

-1/5x+21=7/10x+12

We move all terms to the left:

-1/5x+21-(7/10x+12)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x+12)!=0

x∈R


We get rid of parentheses

-1/5x-7/10x-12+21=0

We calculate fractions


(-10x)/50x^2+(-35x)/50x^2-12+21=0

We add all the numbers together, and all the variables

(-10x)/50x^2+(-35x)/50x^2+9=0

We multiply all the terms by the denominator


(-10x)+(-35x)+9*50x^2=0

Wy multiply elements

450x^2+(-10x)+(-35x)=0

We get rid of parentheses

450x^2-10x-35x=0

We add all the numbers together, and all the variables

450x^2-45x=0

a = 450; b = -45; c = 0;
Δ = b2-4ac
Δ = -452-4·450·0
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-45}{2*450}=\frac{0}{900}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+45}{2*450}=\frac{90}{900}
=1/10
$