10x-17/4x+11=0

Solution for 10x-17/4x+11=0 equation:

10x-17/4x+11=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


10x*4x+11*4x-17=0

Wy multiply elements

40x^2+44x-17=0

a = 40; b = 44; c = -17;
Δ = b2-4ac
Δ = 442-4·40·(-17)
Δ = 4656
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:

$\sqrt{\Delta}=\sqrt{4656}=\sqrt{16*291}=\sqrt{16}*\sqrt{291}=4\sqrt{291}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-4\sqrt{291}}{2*40}=\frac{-44-4\sqrt{291}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+4\sqrt{291}}{2*40}=\frac{-44+4\sqrt{291}}{80}
$