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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

(x-1)+22

We get rid of parentheses

x-1+22

We add all the numbers together, and all the variables

x+21

Back to the equation:

-(x+21)


We get rid of parentheses

4x^2+28x-x-21=0

We add all the numbers together, and all the variables

4x^2+27x-21=0

a = 4; b = 27; c = -21;
Δ = b2-4ac
Δ = 272-4·4·(-21)
Δ = 1065
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{-(27)-\sqrt{1065}}{2*4}=\frac{-27-\sqrt{1065}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+\sqrt{1065}}{2*4}=\frac{-27+\sqrt{1065}}{8}
$