(x+1)/2-3x(x-1)=(-6(x-1)(x+1)-5)/2

Solution for (x+1)/2-3x(x-1)=(-6(x-1)(x+1)-5)/2 equation:

(x+1)/2-3x(x-1)=(-6(x-1)(x+1)-5)/2

We move all terms to the left:

(x+1)/2-3x(x-1)-((-6(x-1)(x+1)-5)/2)=0

We use the square of the difference formula

x^2+(x+1)/2-3x(x-1)+1=0

We multiply parentheses

x^2-3x^2+(x+1)/2+3x+1=0

We multiply all the terms by the denominator


x^2*2-3x^2*2+(x+1)+3x*2+1*2=0

We add all the numbers together, and all the variables

x^2*2-3x^2*2+(x+1)+3x*2+2=0

Wy multiply elements

2x^2-6x^2+(x+1)+6x+2=0

We get rid of parentheses

2x^2-6x^2+x+6x+1+2=0

We add all the numbers together, and all the variables

-4x^2+7x+3=0

a = -4; b = 7; c = +3;
Δ = b2-4ac
Δ = 72-4·(-4)·3
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{97}}{2*-4}=\frac{-7-\sqrt{97}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{97}}{2*-4}=\frac{-7+\sqrt{97}}{-8}
$