-12b^2-10b+1=-8b^2-3b-2

Solution for -12b^2-10b+1=-8b^2-3b-2 equation:

-12b^2-10b+1=-8b^2-3b-2

We move all terms to the left:

-12b^2-10b+1-(-8b^2-3b-2)=0

We get rid of parentheses

-12b^2+8b^2+3b-10b+2+1=0

We add all the numbers together, and all the variables

-4b^2-7b+3=0

a = -4; b = -7; c = +3;
Δ = b2-4ac
Δ = -72-4·(-4)·3
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{97}}{2*-4}=\frac{7-\sqrt{97}}{-8}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{97}}{2*-4}=\frac{7+\sqrt{97}}{-8}
$