37a+1111=5a^2+35a

Solution for 37a+1111=5a^2+35a equation:

37a+1111=5a^2+35a

We move all terms to the left:

37a+1111-(5a^2+35a)=0

We get rid of parentheses

-5a^2+37a-35a+1111=0

We add all the numbers together, and all the variables

-5a^2+2a+1111=0

a = -5; b = 2; c = +1111;
Δ = b2-4ac
Δ = 22-4·(-5)·1111
Δ = 22224
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:

$\sqrt{\Delta}=\sqrt{22224}=\sqrt{16*1389}=\sqrt{16}*\sqrt{1389}=4\sqrt{1389}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4\sqrt{1389}}{2*-5}=\frac{-2-4\sqrt{1389}}{-10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{1389}}{2*-5}=\frac{-2+4\sqrt{1389}}{-10}
$