X^2/4=2x+5

Solution for X^2/4=2x+5 equation:

X^2/4=2X+5

We move all terms to the left:

X^2/4-(2X+5)=0

We get rid of parentheses

X^2/4-2X-5=0

We multiply all the terms by the denominator


X^2-2X*4-5*4=0

We add all the numbers together, and all the variables

X^2-2X*4-20=0

Wy multiply elements

X^2-8X-20=0

a = 1; b = -8; c = -20;
Δ = b2-4ac
Δ = -82-4·1·(-20)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-12}{2*1}=\frac{-4}{2}
=-2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+12}{2*1}=\frac{20}{2}
=10
$