1/4x+7/2x=15

Solution for 1/4x+7/2x=15 equation:

1/4x+7/2x=15

We move all terms to the left:

1/4x+7/2x-(15)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We calculate fractions


2x/8x^2+28x/8x^2-15=0

We multiply all the terms by the denominator


2x+28x-15*8x^2=0

We add all the numbers together, and all the variables

30x-15*8x^2=0

Wy multiply elements

-120x^2+30x=0

a = -120; b = 30; c = 0;
Δ = b2-4ac
Δ = 302-4·(-120)·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30}{2*-120}=\frac{-60}{-240}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30}{2*-120}=\frac{0}{-240}
=0
$