5x2/2=2x+9

Solution for 5x2/2=2x+9 equation:

5x^2/2=2x+9

We move all terms to the left:

5x^2/2-(2x+9)=0

We get rid of parentheses

5x^2/2-2x-9=0

We multiply all the terms by the denominator


5x^2-2x*2-9*2=0

We add all the numbers together, and all the variables

5x^2-2x*2-18=0

Wy multiply elements

5x^2-4x-18=0

a = 5; b = -4; c = -18;
Δ = b2-4ac
Δ = -42-4·5·(-18)
Δ = 376
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:

$\sqrt{\Delta}=\sqrt{376}=\sqrt{4*94}=\sqrt{4}*\sqrt{94}=2\sqrt{94}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{94}}{2*5}=\frac{4-2\sqrt{94}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{94}}{2*5}=\frac{4+2\sqrt{94}}{10}
$