x(.2x+52)=2745

Solution for x(.2x+52)=2745 equation:

x(.2x+52)=2745

We move all terms to the left:

x(.2x+52)-(2745)=0

We multiply parentheses

x^2+52x-2745=0

a = 1; b = 52; c = -2745;
Δ = b2-4ac
Δ = 522-4·1·(-2745)
Δ = 13684
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:

$\sqrt{\Delta}=\sqrt{13684}=\sqrt{4*3421}=\sqrt{4}*\sqrt{3421}=2\sqrt{3421}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-2\sqrt{3421}}{2*1}=\frac{-52-2\sqrt{3421}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+2\sqrt{3421}}{2*1}=\frac{-52+2\sqrt{3421}}{2}
$