7a^2=2a+4

Solution for 7a^2=2a+4 equation:

7a^2=2a+4

We move all terms to the left:

7a^2-(2a+4)=0

We get rid of parentheses

7a^2-2a-4=0

a = 7; b = -2; c = -4;
Δ = b2-4ac
Δ = -22-4·7·(-4)
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{29}}{2*7}=\frac{2-2\sqrt{29}}{14}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{29}}{2*7}=\frac{2+2\sqrt{29}}{14}
$