x^2-2x(7-3x)/2=1

Solution for x^2-2x(7-3x)/2=1 equation:

x^2-2x(7-3x)/2=1

We move all terms to the left:

x^2-2x(7-3x)/2-(1)=0

We add all the numbers together, and all the variables

x^2-2x(-3x+7)/2-1=0

We multiply all the terms by the denominator


x^2*2-2x(-3x+7)-1*2=0

We add all the numbers together, and all the variables

x^2*2-2x(-3x+7)-2=0

We multiply parentheses

x^2*2+6x^2-14x-2=0

Wy multiply elements

2x^2+6x^2-14x-2=0

We add all the numbers together, and all the variables

8x^2-14x-2=0

a = 8; b = -14; c = -2;
Δ = b2-4ac
Δ = -142-4·8·(-2)
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{65}}{2*8}=\frac{14-2\sqrt{65}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{65}}{2*8}=\frac{14+2\sqrt{65}}{16}
$