1=3x-10/2x-3

Solution for 1=3x-10/2x-3 equation:

1=3x-10/2x-3

We move all terms to the left:

1-(3x-10/2x-3)=0


Domain of the equation: 2x-3)!=0

x∈R


We get rid of parentheses

-3x+10/2x+3+1=0

We multiply all the terms by the denominator


-3x*2x+3*2x+1*2x+10=0

Wy multiply elements

-6x^2+6x+2x+10=0

We add all the numbers together, and all the variables

-6x^2+8x+10=0

a = -6; b = 8; c = +10;
Δ = b2-4ac
Δ = 82-4·(-6)·10
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{19}}{2*-6}=\frac{-8-4\sqrt{19}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{19}}{2*-6}=\frac{-8+4\sqrt{19}}{-12}
$