3/4x+2/5x=69

Solution for 3/4x+2/5x=69 equation:

3/4x+2/5x=69

We move all terms to the left:

3/4x+2/5x-(69)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We calculate fractions


15x/20x^2+8x/20x^2-69=0

We multiply all the terms by the denominator


15x+8x-69*20x^2=0

We add all the numbers together, and all the variables

23x-69*20x^2=0

Wy multiply elements

-1380x^2+23x=0

a = -1380; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·(-1380)·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-23}{2*-1380}=\frac{-46}{-2760}
=1/60
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*-1380}=\frac{0}{-2760}
=0
$