13x+30=1/4x+60

Solution for 13x+30=1/4x+60 equation:

13x+30=1/4x+60

We move all terms to the left:

13x+30-(1/4x+60)=0


Domain of the equation: 4x+60)!=0

x∈R


We get rid of parentheses

13x-1/4x-60+30=0

We multiply all the terms by the denominator


13x*4x-60*4x+30*4x-1=0

Wy multiply elements

52x^2-240x+120x-1=0

We add all the numbers together, and all the variables

52x^2-120x-1=0

a = 52; b = -120; c = -1;
Δ = b2-4ac
Δ = -1202-4·52·(-1)
Δ = 14608
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:

$\sqrt{\Delta}=\sqrt{14608}=\sqrt{16*913}=\sqrt{16}*\sqrt{913}=4\sqrt{913}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-4\sqrt{913}}{2*52}=\frac{120-4\sqrt{913}}{104}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+4\sqrt{913}}{2*52}=\frac{120+4\sqrt{913}}{104}
$