3/4x-2+90+2/5x=189

Solution for 3/4x-2+90+2/5x=189 equation:

3/4x-2+90+2/5x=189

We move all terms to the left:

3/4x-2+90+2/5x-(189)=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 add all the numbers together, and all the variables

3/4x+2/5x-101=0

We calculate fractions


15x/20x^2+8x/20x^2-101=0

We multiply all the terms by the denominator


15x+8x-101*20x^2=0

We add all the numbers together, and all the variables

23x-101*20x^2=0

Wy multiply elements

-2020x^2+23x=0

a = -2020; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·(-2020)·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*-2020}=\frac{-46}{-4040}
=23/2020
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*-2020}=\frac{0}{-4040}
=0
$