10(x-2)+13=(5X-1)(1+5X)

Solution for 10(x-2)+13=(5X-1)(1+5X) equation:

10(x-2)+13=(5x-1)(1+5x)

We move all terms to the left:

10(x-2)+13-((5x-1)(1+5x))=0

We add all the numbers together, and all the variables

10(x-2)-((5x-1)(5x+1))+13=0

We use the square of the difference formula

25x^2+10(x-2)+1+13=0

We multiply parentheses

25x^2+10x-20+1+13=0

We add all the numbers together, and all the variables

25x^2+10x-6=0

a = 25; b = 10; c = -6;
Δ = b2-4ac
Δ = 102-4·25·(-6)
Δ = 700
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{700}=\sqrt{100*7}=\sqrt{100}*\sqrt{7}=10\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{7}}{2*25}=\frac{-10-10\sqrt{7}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{7}}{2*25}=\frac{-10+10\sqrt{7}}{50}
$