3/2x-5=4x-11

Solution for 3/2x-5=4x-11 equation:

3/2x-5=4x-11

We move all terms to the left:

3/2x-5-(4x-11)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

3/2x-4x+11-5=0

We multiply all the terms by the denominator


-4x*2x+11*2x-5*2x+3=0

Wy multiply elements

-8x^2+22x-10x+3=0

We add all the numbers together, and all the variables

-8x^2+12x+3=0

a = -8; b = 12; c = +3;
Δ = b2-4ac
Δ = 122-4·(-8)·3
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{15}}{2*-8}=\frac{-12-4\sqrt{15}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{15}}{2*-8}=\frac{-12+4\sqrt{15}}{-16}
$