24a-22=-4(1-6a)1/1

Solution for 24a-22=-4(1-6a)1/1 equation:

24a-22=-4(1-6a)1/1

We move all terms to the left:

24a-22-(-4(1-6a)1/1)=0

We add all the numbers together, and all the variables

24a-(-4(-6a+1)1/1)-22=0

We multiply all the terms by the denominator


24a*1)-(-4(-6a+1)1-22*1)=0

We add all the numbers together, and all the variables

24a*1)-(-4(-6a+1)1=0

We multiply parentheses

24a*1)-(+24a-4=0

Wy multiply elements

24a^2+24a-4=0

a = 24; b = 24; c = -4;
Δ = b2-4ac
Δ = 242-4·24·(-4)
Δ = 960
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8\sqrt{15}}{2*24}=\frac{-24-8\sqrt{15}}{48}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8\sqrt{15}}{2*24}=\frac{-24+8\sqrt{15}}{48}
$