6.94x2+4.13x=9.46

Solution for 6.94x2+4.13x=9.46 equation:

6.94x^2+4.13x=9.46

We move all terms to the left:

6.94x^2+4.13x-(9.46)=0

We add all the numbers together, and all the variables

6.94x^2+4.13x-9.46=0

a = 6.94; b = 4.13; c = -9.46;
Δ = b2-4ac
Δ = 4.132-4·6.94·(-9.46)
Δ = 279.6665
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4.13)-\sqrt{279.6665}}{2*6.94}=\frac{-4.13-\sqrt{279.6665}}{13.88}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4.13)+\sqrt{279.6665}}{2*6.94}=\frac{-4.13+\sqrt{279.6665}}{13.88}
$