65=x(2x+3)

Solution for 65=x(2x+3) equation:

65=x(2x+3)

We move all terms to the left:

65-(x(2x+3))=0


We calculate terms in parentheses: -(x(2x+3)), so:

x(2x+3)

We multiply parentheses

2x^2+3x

Back to the equation:

-(2x^2+3x)


We get rid of parentheses

-2x^2-3x+65=0

a = -2; b = -3; c = +65;
Δ = b2-4ac
Δ = -32-4·(-2)·65
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-23}{2*-2}=\frac{-20}{-4}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+23}{2*-2}=\frac{26}{-4}
=-6+1/2
$