3/5x+1/4x=51

Solution for 3/5x+1/4x=51 equation:

3/5x+1/4x=51

We move all terms to the left:

3/5x+1/4x-(51)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We calculate fractions


12x/20x^2+5x/20x^2-51=0

We multiply all the terms by the denominator


12x+5x-51*20x^2=0

We add all the numbers together, and all the variables

17x-51*20x^2=0

Wy multiply elements

-1020x^2+17x=0

a = -1020; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-1020)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-1020}=\frac{-34}{-2040}
=1/60
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-1020}=\frac{0}{-2040}
=0
$