(4a)=7(5-a^2)=-7

Solution for (4a)=7(5-a^2)=-7 equation:

(4a)=7(5-a^2)=-7

We move all terms to the left:

(4a)-(7(5-a^2))=0


We calculate terms in parentheses: -(7(5-a^2)), so:

7(5-a^2)

We multiply parentheses

-7a^2+35

Back to the equation:

-(-7a^2+35)


We get rid of parentheses

7a^2+4a-35=0

a = 7; b = 4; c = -35;
Δ = b2-4ac
Δ = 42-4·7·(-35)
Δ = 996
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:

$\sqrt{\Delta}=\sqrt{996}=\sqrt{4*249}=\sqrt{4}*\sqrt{249}=2\sqrt{249}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{249}}{2*7}=\frac{-4-2\sqrt{249}}{14}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{249}}{2*7}=\frac{-4+2\sqrt{249}}{14}
$