2x+25-15/10x=3

Solution for 2x+25-15/10x=3 equation:

2x+25-15/10x=3

We move all terms to the left:

2x+25-15/10x-(3)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We add all the numbers together, and all the variables

2x-15/10x+22=0

We multiply all the terms by the denominator


2x*10x+22*10x-15=0

Wy multiply elements

20x^2+220x-15=0

a = 20; b = 220; c = -15;
Δ = b2-4ac
Δ = 2202-4·20·(-15)
Δ = 49600
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:

$\sqrt{\Delta}=\sqrt{49600}=\sqrt{1600*31}=\sqrt{1600}*\sqrt{31}=40\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(220)-40\sqrt{31}}{2*20}=\frac{-220-40\sqrt{31}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(220)+40\sqrt{31}}{2*20}=\frac{-220+40\sqrt{31}}{40}
$