4x^2-130=6x

Solution for 4x^2-130=6x equation:

4x^2-130=6x

We move all terms to the left:

4x^2-130-(6x)=0

a = 4; b = -6; c = -130;
Δ = b2-4ac
Δ = -62-4·4·(-130)
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-46}{2*4}=\frac{-40}{8}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+46}{2*4}=\frac{52}{8}
=6+1/2
$