10-(2x-3)(2x-3)=1

Solution for 10-(2x-3)(2x-3)=1 equation:

10-(2x-3)(2x-3)=1

We move all terms to the left:

10-(2x-3)(2x-3)-(1)=0

We add all the numbers together, and all the variables

-(2x-3)(2x-3)+9=0

We multiply parentheses ..

-(+4x^2-6x-6x+9)+9=0

We get rid of parentheses

-4x^2+6x+6x-9+9=0

We add all the numbers together, and all the variables

-4x^2+12x=0

a = -4; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·(-4)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*-4}=\frac{-24}{-8}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-4}=\frac{0}{-8}
=0
$