4k^2-126=10k

Solution for 4k^2-126=10k equation:

4k^2-126=10k

We move all terms to the left:

4k^2-126-(10k)=0

a = 4; b = -10; c = -126;
Δ = b2-4ac
Δ = -102-4·4·(-126)
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-46}{2*4}=\frac{-36}{8}
=-4+1/2
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+46}{2*4}=\frac{56}{8}
=7
$