2x(x+1)=45

Solution for 2x(x+1)=45 equation:

2x(x+1)=45

We move all terms to the left:

2x(x+1)-(45)=0

We multiply parentheses

2x^2+2x-45=0

a = 2; b = 2; c = -45;
Δ = b2-4ac
Δ = 22-4·2·(-45)
Δ = 364
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{91}}{2*2}=\frac{-2-2\sqrt{91}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{91}}{2*2}=\frac{-2+2\sqrt{91}}{4}
$