3/2x-5=7-4x

Solution for 3/2x-5=7-4x equation:

3/2x-5=7-4x

We move all terms to the left:

3/2x-5-(7-4x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3/2x-(-4x+7)-5=0

We get rid of parentheses

3/2x+4x-7-5=0

We multiply all the terms by the denominator


4x*2x-7*2x-5*2x+3=0

Wy multiply elements

8x^2-14x-10x+3=0

We add all the numbers together, and all the variables

8x^2-24x+3=0

a = 8; b = -24; c = +3;
Δ = b2-4ac
Δ = -242-4·8·3
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{30}}{2*8}=\frac{24-4\sqrt{30}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{30}}{2*8}=\frac{24+4\sqrt{30}}{16}
$