2x(x+5)=46

Solution for 2x(x+5)=46 equation:

2x(x+5)=46

We move all terms to the left:

2x(x+5)-(46)=0

We multiply parentheses

2x^2+10x-46=0

a = 2; b = 10; c = -46;
Δ = b2-4ac
Δ = 102-4·2·(-46)
Δ = 468
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:

$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-6\sqrt{13}}{2*2}=\frac{-10-6\sqrt{13}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+6\sqrt{13}}{2*2}=\frac{-10+6\sqrt{13}}{4}
$