3x^2-7x-12.25=16.25

Solution for 3x^2-7x-12.25=16.25 equation:

3x^2-7x-12.25=16.25

We move all terms to the left:

3x^2-7x-12.25-(16.25)=0

We add all the numbers together, and all the variables

3x^2-7x-28.5=0

a = 3; b = -7; c = -28.5;
Δ = b2-4ac
Δ = -72-4·3·(-28.5)
Δ = 391
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{-(-7)-\sqrt{391}}{2*3}=\frac{7-\sqrt{391}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{391}}{2*3}=\frac{7+\sqrt{391}}{6}
$