6.5x+0.6x2=58

Solution for 6.5x+0.6x2=58 equation:

6.5x+0.6x^2=58

We move all terms to the left:

6.5x+0.6x^2-(58)=0

a = 0.6; b = 6.5; c = -58;
Δ = b2-4ac
Δ = 6.52-4·0.6·(-58)
Δ = 181.45
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{-(6.5)-\sqrt{181.45}}{2*0.6}=\frac{-6.5-\sqrt{181.45}}{1.2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6.5)+\sqrt{181.45}}{2*0.6}=\frac{-6.5+\sqrt{181.45}}{1.2}
$