x*2x+1=74

Solution for x*2x+1=74 equation:

x*2x+1=74

We move all terms to the left:

x*2x+1-(74)=0

We add all the numbers together, and all the variables

x*2x-73=0

Wy multiply elements

2x^2-73=0

a = 2; b = 0; c = -73;
Δ = b2-4ac
Δ = 02-4·2·(-73)
Δ = 584
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:

$\sqrt{\Delta}=\sqrt{584}=\sqrt{4*146}=\sqrt{4}*\sqrt{146}=2\sqrt{146}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{146}}{2*2}=\frac{0-2\sqrt{146}}{4}
=-\frac{2\sqrt{146}}{4}
=-\frac{\sqrt{146}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{146}}{2*2}=\frac{0+2\sqrt{146}}{4}
=\frac{2\sqrt{146}}{4}
=\frac{\sqrt{146}}{2}
$