4x-7/5x=3

Solution for 4x-7/5x=3 equation:

4x-7/5x=3

We move all terms to the left:

4x-7/5x-(3)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


4x*5x-3*5x-7=0

Wy multiply elements

20x^2-15x-7=0

a = 20; b = -15; c = -7;
Δ = b2-4ac
Δ = -152-4·20·(-7)
Δ = 785
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{785}}{2*20}=\frac{15-\sqrt{785}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{785}}{2*20}=\frac{15+\sqrt{785}}{40}
$