2x(x+10)=x+23

Solution for 2x(x+10)=x+23 equation:

2x(x+10)=x+23

We move all terms to the left:

2x(x+10)-(x+23)=0

We multiply parentheses

2x^2+20x-(x+23)=0

We get rid of parentheses

2x^2+20x-x-23=0

We add all the numbers together, and all the variables

2x^2+19x-23=0

a = 2; b = 19; c = -23;
Δ = b2-4ac
Δ = 192-4·2·(-23)
Δ = 545
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-\sqrt{545}}{2*2}=\frac{-19-\sqrt{545}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{545}}{2*2}=\frac{-19+\sqrt{545}}{4}
$