/10x+1=8x+15

Solution for /10x+1=8x+15 equation:

/10x+1=8x+15

We move all terms to the left:

/10x+1-(8x+15)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We get rid of parentheses

/10x-8x-15+1=0

We multiply all the terms by the denominator


-8x*10x-15*10x+1*10x+=0

We add all the numbers together, and all the variables

-8x*10x-15*10x+1*10x=0

Wy multiply elements

-80x^2-150x+10x=0

We add all the numbers together, and all the variables

-80x^2-140x=0

a = -80; b = -140; c = 0;
Δ = b2-4ac
Δ = -1402-4·(-80)·0
Δ = 19600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{19600}=140$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-140}{2*-80}=\frac{0}{-160}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+140}{2*-80}=\frac{280}{-160}
=-1+3/4
$