3/4*x+4/5*x=2

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

3/4x+4/5x=2

We move all terms to the left:

3/4x+4/5x-(2)=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+16x/20x^2-2=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

31x-2*20x^2=0

Wy multiply elements

-40x^2+31x=0

a = -40; b = 31; c = 0;
Δ = b2-4ac
Δ = 312-4·(-40)·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*-40}=\frac{-62}{-80}
=31/40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+31}{2*-40}=\frac{0}{-80}
=0
$