6x^2+4x=58

Solution for 6x^2+4x=58 equation:

6x^2+4x=58

We move all terms to the left:

6x^2+4x-(58)=0

a = 6; b = 4; c = -58;
Δ = b2-4ac
Δ = 42-4·6·(-58)
Δ = 1408
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1408}=\sqrt{64*22}=\sqrt{64}*\sqrt{22}=8\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8\sqrt{22}}{2*6}=\frac{-4-8\sqrt{22}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8\sqrt{22}}{2*6}=\frac{-4+8\sqrt{22}}{12}
$