(15/4)x-1/12=7x

Solution for (15/4)x-1/12=7x equation:

(15/4)x-1/12=7x

We move all terms to the left:

(15/4)x-1/12-(7x)=0


Domain of the equation: 4)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+15/4)x-7x-1/12=0

We add all the numbers together, and all the variables

-7x+(+15/4)x-1/12=0

We multiply parentheses

15x^2-7x-1/12=0

We multiply all the terms by the denominator


15x^2*12-7x*12-1=0

Wy multiply elements

180x^2-84x-1=0

a = 180; b = -84; c = -1;
Δ = b2-4ac
Δ = -842-4·180·(-1)
Δ = 7776
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:

$\sqrt{\Delta}=\sqrt{7776}=\sqrt{1296*6}=\sqrt{1296}*\sqrt{6}=36\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-36\sqrt{6}}{2*180}=\frac{84-36\sqrt{6}}{360}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+36\sqrt{6}}{2*180}=\frac{84+36\sqrt{6}}{360}
$