7x/2x^2-15=1

Solution for 7x/2x^2-15=1 equation:

7x/2x^2-15=1

We move all terms to the left:

7x/2x^2-15-(1)=0


Domain of the equation: 2x^2!=0

x^2!=0/2

x^2!=√0

x!=0

x∈R


We add all the numbers together, and all the variables

7x/2x^2-16=0

We multiply all the terms by the denominator


7x-16*2x^2=0

Wy multiply elements

-32x^2+7x=0

a = -32; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-32)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-32}=\frac{-14}{-64}
=7/32
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-32}=\frac{0}{-64}
=0
$