3/2x+2=1-5x+9

Solution for 3/2x+2=1-5x+9 equation:

3/2x+2=1-5x+9

We move all terms to the left:

3/2x+2-(1-5x+9)=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-(-5x+10)+2=0

We get rid of parentheses

3/2x+5x-10+2=0

We multiply all the terms by the denominator


5x*2x-10*2x+2*2x+3=0

Wy multiply elements

10x^2-20x+4x+3=0

We add all the numbers together, and all the variables

10x^2-16x+3=0

a = 10; b = -16; c = +3;
Δ = b2-4ac
Δ = -162-4·10·3
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{34}}{2*10}=\frac{16-2\sqrt{34}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{34}}{2*10}=\frac{16+2\sqrt{34}}{20}
$