x(x+1)=10(2x+1)+56

Solution for x(x+1)=10(2x+1)+56 equation:

x(x+1)=10(2x+1)+56

We move all terms to the left:

x(x+1)-(10(2x+1)+56)=0

We multiply parentheses

x^2+x-(10(2x+1)+56)=0


We calculate terms in parentheses: -(10(2x+1)+56), so:

10(2x+1)+56

We multiply parentheses

20x+10+56

We add all the numbers together, and all the variables

20x+66

Back to the equation:

-(20x+66)


We get rid of parentheses

x^2+x-20x-66=0

We add all the numbers together, and all the variables

x^2-19x-66=0

a = 1; b = -19; c = -66;
Δ = b2-4ac
Δ = -192-4·1·(-66)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-25}{2*1}=\frac{-6}{2}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+25}{2*1}=\frac{44}{2}
=22
$