1/9x+7=15x=

Solution for 1/9x+7=15x= equation:

1/9x+7=15x=

We move all terms to the left:

1/9x+7-(15x)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

-15x+1/9x+7=0

We multiply all the terms by the denominator


-15x*9x+7*9x+1=0

Wy multiply elements

-135x^2+63x+1=0

a = -135; b = 63; c = +1;
Δ = b2-4ac
Δ = 632-4·(-135)·1
Δ = 4509
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:

$\sqrt{\Delta}=\sqrt{4509}=\sqrt{9*501}=\sqrt{9}*\sqrt{501}=3\sqrt{501}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-3\sqrt{501}}{2*-135}=\frac{-63-3\sqrt{501}}{-270}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+3\sqrt{501}}{2*-135}=\frac{-63+3\sqrt{501}}{-270}
$