7k^2+5k-3=4k^2+7k+1

Solution for 7k^2+5k-3=4k^2+7k+1 equation:

7k^2+5k-3=4k^2+7k+1

We move all terms to the left:

7k^2+5k-3-(4k^2+7k+1)=0

We get rid of parentheses

7k^2-4k^2+5k-7k-1-3=0

We add all the numbers together, and all the variables

3k^2-2k-4=0

a = 3; b = -2; c = -4;
Δ = b2-4ac
Δ = -22-4·3·(-4)
Δ = 52
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{13}}{2*3}=\frac{2-2\sqrt{13}}{6}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{13}}{2*3}=\frac{2+2\sqrt{13}}{6}
$