2x(x+3)=x*x+91

Solution for 2x(x+3)=x*x+91 equation:

2x(x+3)=x*x+91

We move all terms to the left:

2x(x+3)-(x*x+91)=0

We multiply parentheses

2x^2+6x-(x*x+91)=0

We get rid of parentheses

2x^2+6x-x*x-91=0

Wy multiply elements

2x^2-1x^2+6x-91=0

We add all the numbers together, and all the variables

x^2+6x-91=0

a = 1; b = 6; c = -91;
Δ = b2-4ac
Δ = 62-4·1·(-91)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-20}{2*1}=\frac{-26}{2}
=-13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+20}{2*1}=\frac{14}{2}
=7
$