-3k+4(6k+2)=-4(8+6k)5k

Solution for -3k+4(6k+2)=-4(8+6k)5k equation:

-3k+4(6k+2)=-4(8+6k)5k

We move all terms to the left:

-3k+4(6k+2)-(-4(8+6k)5k)=0

We add all the numbers together, and all the variables

-3k+4(6k+2)-(-4(6k+8)5k)=0

We multiply parentheses

-3k+24k-(-4(6k+8)5k)+8=0


We calculate terms in parentheses: -(-4(6k+8)5k), so:

-4(6k+8)5k

We multiply parentheses

-120k^2-160k

Back to the equation:

-(-120k^2-160k)


We add all the numbers together, and all the variables

-(-120k^2-160k)+21k+8=0

We get rid of parentheses

120k^2+160k+21k+8=0

We add all the numbers together, and all the variables

120k^2+181k+8=0

a = 120; b = 181; c = +8;
Δ = b2-4ac
Δ = 1812-4·120·8
Δ = 28921
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(181)-\sqrt{28921}}{2*120}=\frac{-181-\sqrt{28921}}{240}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(181)+\sqrt{28921}}{2*120}=\frac{-181+\sqrt{28921}}{240}
$