6x^2+8x=194

Solution for 6x^2+8x=194 equation:

6x^2+8x=194

We move all terms to the left:

6x^2+8x-(194)=0

a = 6; b = 8; c = -194;
Δ = b2-4ac
Δ = 82-4·6·(-194)
Δ = 4720
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:

$\sqrt{\Delta}=\sqrt{4720}=\sqrt{16*295}=\sqrt{16}*\sqrt{295}=4\sqrt{295}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{295}}{2*6}=\frac{-8-4\sqrt{295}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{295}}{2*6}=\frac{-8+4\sqrt{295}}{12}
$