4x(x+7)=9(x-1)+22

Solution for 4x(x+7)=9(x-1)+22 equation:

4x(x+7)=9(x-1)+22

We move all terms to the left:

4x(x+7)-(9(x-1)+22)=0

We multiply parentheses

4x^2+28x-(9(x-1)+22)=0


We calculate terms in parentheses: -(9(x-1)+22), so:

9(x-1)+22

We multiply parentheses

9x-9+22

We add all the numbers together, and all the variables

9x+13

Back to the equation:

-(9x+13)


We get rid of parentheses

4x^2+28x-9x-13=0

We add all the numbers together, and all the variables

4x^2+19x-13=0

a = 4; b = 19; c = -13;
Δ = b2-4ac
Δ = 192-4·4·(-13)
Δ = 569
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-\sqrt{569}}{2*4}=\frac{-19-\sqrt{569}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{569}}{2*4}=\frac{-19+\sqrt{569}}{8}
$