(X+19)(5x-4=1)

Solution for (X+19)(5x-4=1) equation:

(X+19)(5X-4=1)

We move all terms to the left:

(X+19)(5X-4-(1))=0

We add all the numbers together, and all the variables

(X+19)(5X-5)=0

We multiply parentheses ..

(+5X^2-5X+95X-95)=0

We get rid of parentheses

5X^2-5X+95X-95=0

We add all the numbers together, and all the variables

5X^2+90X-95=0

a = 5; b = 90; c = -95;
Δ = b2-4ac
Δ = 902-4·5·(-95)
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-100}{2*5}=\frac{-190}{10}
=-19
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+100}{2*5}=\frac{10}{10}
=1
$