4x=6x^2-130

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

4x=6x^2-130

We move all terms to the left:

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

We get rid of parentheses

-6x^2+4x+130=0

a = -6; b = 4; c = +130;
Δ = b2-4ac
Δ = 42-4·(-6)·130
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-56}{2*-6}=\frac{-60}{-12}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+56}{2*-6}=\frac{52}{-12}
=-4+1/3
$