7a^2-7=-48a

Solution for 7a^2-7=-48a equation:

7a^2-7=-48a

We move all terms to the left:

7a^2-7-(-48a)=0

We get rid of parentheses

7a^2+48a-7=0

a = 7; b = 48; c = -7;
Δ = b2-4ac
Δ = 482-4·7·(-7)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-50}{2*7}=\frac{-98}{14}
=-7
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+50}{2*7}=\frac{2}{14}
=1/7
$