x(2x+3)=2x^+9

Solution for x(2x+3)=2x^+9 equation:

x(2x+3)=2x^+9

We move all terms to the left:

x(2x+3)-(2x^+9)=0

We multiply parentheses

2x^2+3x-(2x^+9)=0

We get rid of parentheses

2x^2+3x-2x^-9=0

We add all the numbers together, and all the variables

2x^2+x-9=0

a = 2; b = 1; c = -9;
Δ = b2-4ac
Δ = 12-4·2·(-9)
Δ = 73
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{-(1)-\sqrt{73}}{2*2}=\frac{-1-\sqrt{73}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{73}}{2*2}=\frac{-1+\sqrt{73}}{4}
$