x(2x+10)=546

Solution for x(2x+10)=546 equation:

x(2x+10)=546

We move all terms to the left:

x(2x+10)-(546)=0

We multiply parentheses

2x^2+10x-546=0

a = 2; b = 10; c = -546;
Δ = b2-4ac
Δ = 102-4·2·(-546)
Δ = 4468
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:

$\sqrt{\Delta}=\sqrt{4468}=\sqrt{4*1117}=\sqrt{4}*\sqrt{1117}=2\sqrt{1117}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{1117}}{2*2}=\frac{-10-2\sqrt{1117}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{1117}}{2*2}=\frac{-10+2\sqrt{1117}}{4}
$