(2x-3)(2x-3)-49=0

Solution for (2x-3)(2x-3)-49=0 equation:

(2x-3)(2x-3)-49=0

We multiply parentheses ..

(+4x^2-6x-6x+9)-49=0

We get rid of parentheses

4x^2-6x-6x+9-49=0

We add all the numbers together, and all the variables

4x^2-12x-40=0

a = 4; b = -12; c = -40;
Δ = b2-4ac
Δ = -122-4·4·(-40)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-28}{2*4}=\frac{-16}{8}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+28}{2*4}=\frac{40}{8}
=5
$