1/7x+9=10x+72

Solution for 1/7x+9=10x+72 equation:

1/7x+9=10x+72

We move all terms to the left:

1/7x+9-(10x+72)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

1/7x-10x-72+9=0

We multiply all the terms by the denominator


-10x*7x-72*7x+9*7x+1=0

Wy multiply elements

-70x^2-504x+63x+1=0

We add all the numbers together, and all the variables

-70x^2-441x+1=0

a = -70; b = -441; c = +1;
Δ = b2-4ac
Δ = -4412-4·(-70)·1
Δ = 194761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-441)-\sqrt{194761}}{2*-70}=\frac{441-\sqrt{194761}}{-140}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-441)+\sqrt{194761}}{2*-70}=\frac{441+\sqrt{194761}}{-140}
$