x+11/4x=7590

Solution for x+11/4x=7590 equation:

x+11/4x=7590

We move all terms to the left:

x+11/4x-(7590)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


x*4x-7590*4x+11=0

Wy multiply elements

4x^2-30360x+11=0

a = 4; b = -30360; c = +11;
Δ = b2-4ac
Δ = -303602-4·4·11
Δ = 921729424
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:

$\sqrt{\Delta}=\sqrt{921729424}=\sqrt{16*57608089}=\sqrt{16}*\sqrt{57608089}=4\sqrt{57608089}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30360)-4\sqrt{57608089}}{2*4}=\frac{30360-4\sqrt{57608089}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30360)+4\sqrt{57608089}}{2*4}=\frac{30360+4\sqrt{57608089}}{8}
$