8b^2+41b+15=-6b^2

Solution for 8b^2+41b+15=-6b^2 equation:

8b^2+41b+15=-6b^2

We move all terms to the left:

8b^2+41b+15-(-6b^2)=0

We get rid of parentheses

8b^2+6b^2+41b+15=0

We add all the numbers together, and all the variables

14b^2+41b+15=0

a = 14; b = 41; c = +15;
Δ = b2-4ac
Δ = 412-4·14·15
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-29}{2*14}=\frac{-70}{28}
=-2+1/2
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+29}{2*14}=\frac{-12}{28}
=-3/7
$