(2x-1)(x)=45

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Solution for (2x-1)(x)=45 equation:



(2x-1)(x)=45
We move all terms to the left:
(2x-1)(x)-(45)=0
We multiply parentheses
2x^2-1x-45=0
a = 2; b = -1; c = -45;
Δ = b2-4ac
Δ = -12-4·2·(-45)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-19}{2*2}=\frac{-18}{4} =-4+1/2 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+19}{2*2}=\frac{20}{4} =5 $

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