5x+3/4x=58

Solution for 5x+3/4x=58 equation:

5x+3/4x=58

We move all terms to the left:

5x+3/4x-(58)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


5x*4x-58*4x+3=0

Wy multiply elements

20x^2-232x+3=0

a = 20; b = -232; c = +3;
Δ = b2-4ac
Δ = -2322-4·20·3
Δ = 53584
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{53584}=\sqrt{16*3349}=\sqrt{16}*\sqrt{3349}=4\sqrt{3349}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-232)-4\sqrt{3349}}{2*20}=\frac{232-4\sqrt{3349}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-232)+4\sqrt{3349}}{2*20}=\frac{232+4\sqrt{3349}}{40}
$