3b^2+24b+43=7

Solution for 3b^2+24b+43=7 equation:

3b^2+24b+43=7

We move all terms to the left:

3b^2+24b+43-(7)=0

We add all the numbers together, and all the variables

3b^2+24b+36=0

a = 3; b = 24; c = +36;
Δ = b2-4ac
Δ = 242-4·3·36
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-12}{2*3}=\frac{-36}{6}
=-6
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+12}{2*3}=\frac{-12}{6}
=-2
$