-38x+21=12-8x^2

Solution for -38x+21=12-8x^2 equation:

-38x+21=12-8x^2

We move all terms to the left:

-38x+21-(12-8x^2)=0

We get rid of parentheses

8x^2-38x-12+21=0

We add all the numbers together, and all the variables

8x^2-38x+9=0

a = 8; b = -38; c = +9;
Δ = b2-4ac
Δ = -382-4·8·9
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-34}{2*8}=\frac{4}{16}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+34}{2*8}=\frac{72}{16}
=4+1/2
$