4x-3x^2=-3.5

Solution for 4x-3x^2=-3.5 equation:

4x-3x^2=-3.5

We move all terms to the left:

4x-3x^2-(-3.5)=0

We add all the numbers together, and all the variables

-3x^2+4x+3.5=0

a = -3; b = 4; c = +3.5;
Δ = b2-4ac
Δ = 42-4·(-3)·3.5
Δ = 58
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)-\sqrt{58}}{2*-3}=\frac{-4-\sqrt{58}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+\sqrt{58}}{2*-3}=\frac{-4+\sqrt{58}}{-6}
$