5x+3x/4x=10

Solution for 5x+3x/4x=10 equation:

5x+3x/4x=10

We move all terms to the left:

5x+3x/4x-(10)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


5x*4x+3x-10*4x=0

We add all the numbers together, and all the variables

3x+5x*4x-10*4x=0

Wy multiply elements

20x^2+3x-40x=0

We add all the numbers together, and all the variables

20x^2-37x=0

a = 20; b = -37; c = 0;
Δ = b2-4ac
Δ = -372-4·20·0
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-37}{2*20}=\frac{0}{40}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+37}{2*20}=\frac{74}{40}
=1+17/20
$