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

Solution for (2x-9)(2x-9)=x+3 equation:

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

We move all terms to the left:

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

We get rid of parentheses

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

We multiply parentheses ..

(+4x^2-18x-18x+81)-x-3=0

We add all the numbers together, and all the variables

(+4x^2-18x-18x+81)-1x-3=0

We get rid of parentheses

4x^2-18x-18x-1x+81-3=0

We add all the numbers together, and all the variables

4x^2-37x+78=0

a = 4; b = -37; c = +78;
Δ = b2-4ac
Δ = -372-4·4·78
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-11}{2*4}=\frac{26}{8}
=3+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+11}{2*4}=\frac{48}{8}
=6
$