4x^2=22-3x

Solution for 4x^2=22-3x equation:

4x^2=22-3x

We move all terms to the left:

4x^2-(22-3x)=0

We add all the numbers together, and all the variables

4x^2-(-3x+22)=0

We get rid of parentheses

4x^2+3x-22=0

a = 4; b = 3; c = -22;
Δ = b2-4ac
Δ = 32-4·4·(-22)
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{-(3)-19}{2*4}=\frac{-22}{8}
=-2+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+19}{2*4}=\frac{16}{8}
=2
$