4a2+14a-55=3a2+8a

Solution for 4a2+14a-55=3a2+8a equation:

4a^2+14a-55=3a^2+8a

We move all terms to the left:

4a^2+14a-55-(3a^2+8a)=0

We get rid of parentheses

4a^2-3a^2+14a-8a-55=0

We add all the numbers together, and all the variables

a^2+6a-55=0

a = 1; b = 6; c = -55;
Δ = b2-4ac
Δ = 62-4·1·(-55)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-16}{2*1}=\frac{-22}{2}
=-11
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+16}{2*1}=\frac{10}{2}
=5
$