8-6(x-4)=2x(4x-5)+22

Solution for 8-6(x-4)=2x(4x-5)+22 equation:

8-6(x-4)=2x(4x-5)+22

We move all terms to the left:

8-6(x-4)-(2x(4x-5)+22)=0

We multiply parentheses

-6x-(2x(4x-5)+22)+24+8=0


We calculate terms in parentheses: -(2x(4x-5)+22), so:

2x(4x-5)+22

We multiply parentheses

8x^2-10x+22

Back to the equation:

-(8x^2-10x+22)


We add all the numbers together, and all the variables

-6x-(8x^2-10x+22)+32=0

We get rid of parentheses

-8x^2-6x+10x-22+32=0

We add all the numbers together, and all the variables

-8x^2+4x+10=0

a = -8; b = 4; c = +10;
Δ = b2-4ac
Δ = 42-4·(-8)·10
Δ = 336
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{21}}{2*-8}=\frac{-4-4\sqrt{21}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{21}}{2*-8}=\frac{-4+4\sqrt{21}}{-16}
$