5x(x+5)=x+57

Solution for 5x(x+5)=x+57 equation:

5x(x+5)=x+57

We move all terms to the left:

5x(x+5)-(x+57)=0

We multiply parentheses

5x^2+25x-(x+57)=0

We get rid of parentheses

5x^2+25x-x-57=0

We add all the numbers together, and all the variables

5x^2+24x-57=0

a = 5; b = 24; c = -57;
Δ = b2-4ac
Δ = 242-4·5·(-57)
Δ = 1716
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:

$\sqrt{\Delta}=\sqrt{1716}=\sqrt{4*429}=\sqrt{4}*\sqrt{429}=2\sqrt{429}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{429}}{2*5}=\frac{-24-2\sqrt{429}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{429}}{2*5}=\frac{-24+2\sqrt{429}}{10}
$