4/x+7/2x=15/16

Solution for 4/x+7/2x=15/16 equation:

4/x+7/2x=15/16

We move all terms to the left:

4/x+7/2x-(15/16)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

4/x+7/2x-(+15/16)=0

We get rid of parentheses

4/x+7/2x-15/16=0

We calculate fractions


(-60x^2)/32x^2+128x/32x^2+112x/32x^2=0

We multiply all the terms by the denominator


(-60x^2)+128x+112x=0

We add all the numbers together, and all the variables

(-60x^2)+240x=0

We get rid of parentheses

-60x^2+240x=0

a = -60; b = 240; c = 0;
Δ = b2-4ac
Δ = 2402-4·(-60)·0
Δ = 57600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{57600}=240$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(240)-240}{2*-60}=\frac{-480}{-120}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(240)+240}{2*-60}=\frac{0}{-120}
=0
$