6,7x+1,2x^2=11,6

Solution for 6,7x+1,2x^2=11,6 equation:

6.7x+1.2x^2=11.6

We move all terms to the left:

6.7x+1.2x^2-(11.6)=0

We add all the numbers together, and all the variables

1.2x^2+6.7x-11.6=0

a = 1.2; b = 6.7; c = -11.6;
Δ = b2-4ac
Δ = 6.72-4·1.2·(-11.6)
Δ = 100.57
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{-(6.7)-\sqrt{100.57}}{2*1.2}=\frac{-6.7-\sqrt{100.57}}{2.4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6.7)+\sqrt{100.57}}{2*1.2}=\frac{-6.7+\sqrt{100.57}}{2.4}
$