8x+4=3x^2-0.75

Solution for 8x+4=3x^2-0.75 equation:

8x+4=3x^2-0.75

We move all terms to the left:

8x+4-(3x^2-0.75)=0

We get rid of parentheses

-3x^2+8x+0.75+4=0

We add all the numbers together, and all the variables

-3x^2+8x+4.75=0

a = -3; b = 8; c = +4.75;
Δ = b2-4ac
Δ = 82-4·(-3)·4.75
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-11}{2*-3}=\frac{-19}{-6}
=3+1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+11}{2*-3}=\frac{3}{-6}
=-1/2
$