x(2x-174)=-1048

Solution for x(2x-174)=-1048 equation:

x(2x-174)=-1048

We move all terms to the left:

x(2x-174)-(-1048)=0

We add all the numbers together, and all the variables

x(2x-174)+1048=0

We multiply parentheses

2x^2-174x+1048=0

a = 2; b = -174; c = +1048;
Δ = b2-4ac
Δ = -1742-4·2·1048
Δ = 21892
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:

$\sqrt{\Delta}=\sqrt{21892}=\sqrt{4*5473}=\sqrt{4}*\sqrt{5473}=2\sqrt{5473}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-174)-2\sqrt{5473}}{2*2}=\frac{174-2\sqrt{5473}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-174)+2\sqrt{5473}}{2*2}=\frac{174+2\sqrt{5473}}{4}
$