4x^2=5-x

Solution for 4x^2=5-x equation:

4x^2=5-x

We move all terms to the left:

4x^2-(5-x)=0

We add all the numbers together, and all the variables

4x^2-(-1x+5)=0

We get rid of parentheses

4x^2+1x-5=0

We add all the numbers together, and all the variables

4x^2+x-5=0

a = 4; b = 1; c = -5;
Δ = b2-4ac
Δ = 12-4·4·(-5)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-9}{2*4}=\frac{-10}{8}
=-1+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+9}{2*4}=\frac{8}{8}
=1
$