7a^2=48+58a

Solution for 7a^2=48+58a equation:

7a^2=48+58a

We move all terms to the left:

7a^2-(48+58a)=0

We add all the numbers together, and all the variables

7a^2-(58a+48)=0

We get rid of parentheses

7a^2-58a-48=0

a = 7; b = -58; c = -48;
Δ = b2-4ac
Δ = -582-4·7·(-48)
Δ = 4708
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4708}=\sqrt{4*1177}=\sqrt{4}*\sqrt{1177}=2\sqrt{1177}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-58)-2\sqrt{1177}}{2*7}=\frac{58-2\sqrt{1177}}{14}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-58)+2\sqrt{1177}}{2*7}=\frac{58+2\sqrt{1177}}{14}
$