4/5x+3/4x=5

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

4/5x+3/4x=5

We move all terms to the left:

4/5x+3/4x-(5)=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


16x/20x^2+15x/20x^2-5=0

We multiply all the terms by the denominator


16x+15x-5*20x^2=0

We add all the numbers together, and all the variables

31x-5*20x^2=0

Wy multiply elements

-100x^2+31x=0

a = -100; b = 31; c = 0;
Δ = b2-4ac
Δ = 312-4·(-100)·0
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-31}{2*-100}=\frac{-62}{-200}
=31/100
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+31}{2*-100}=\frac{0}{-200}
=0
$