7x-45/4x=-2

Solution for 7x-45/4x=-2 equation:

7x-45/4x=-2

We move all terms to the left:

7x-45/4x-(-2)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

7x-45/4x+2=0

We multiply all the terms by the denominator


7x*4x+2*4x-45=0

Wy multiply elements

28x^2+8x-45=0

a = 28; b = 8; c = -45;
Δ = b2-4ac
Δ = 82-4·28·(-45)
Δ = 5104
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:

$\sqrt{\Delta}=\sqrt{5104}=\sqrt{16*319}=\sqrt{16}*\sqrt{319}=4\sqrt{319}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{319}}{2*28}=\frac{-8-4\sqrt{319}}{56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{319}}{2*28}=\frac{-8+4\sqrt{319}}{56}
$