15-6x/2x-5=4x-10

Solution for 15-6x/2x-5=4x-10 equation:

15-6x/2x-5=4x-10

We move all terms to the left:

15-6x/2x-5-(4x-10)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-6x/2x-(4x-10)+10=0

We get rid of parentheses

-6x/2x-4x+10+10=0

We multiply all the terms by the denominator


-6x-4x*2x+10*2x+10*2x=0

Wy multiply elements

-8x^2-6x+20x+20x=0

We add all the numbers together, and all the variables

-8x^2+34x=0

a = -8; b = 34; c = 0;
Δ = b2-4ac
Δ = 342-4·(-8)·0
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-34}{2*-8}=\frac{-68}{-16}
=4+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+34}{2*-8}=\frac{0}{-16}
=0
$