(5x-19)(5x-19)=121

Solution for (5x-19)(5x-19)=121 equation:

(5x-19)(5x-19)=121

We move all terms to the left:

(5x-19)(5x-19)-(121)=0

We multiply parentheses ..

(+25x^2-95x-95x+361)-121=0

We get rid of parentheses

25x^2-95x-95x+361-121=0

We add all the numbers together, and all the variables

25x^2-190x+240=0

a = 25; b = -190; c = +240;
Δ = b2-4ac
Δ = -1902-4·25·240
Δ = 12100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12100}=110$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-190)-110}{2*25}=\frac{80}{50}
=1+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-190)+110}{2*25}=\frac{300}{50}
=6
$