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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} $
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