(a*a)-(11*a)=840

Solution for (a*a)-(11*a)=840 equation:

(a*a)-(11a)=840

We move all terms to the left:

(a*a)-(11a)-(840)=0

We add all the numbers together, and all the variables

(+a*a)-11a-840=0

We add all the numbers together, and all the variables

-11a+(+a*a)-840=0

We get rid of parentheses

-11a+a*a-840=0

Wy multiply elements

a^2-11a-840=0

a = 1; b = -11; c = -840;
Δ = b2-4ac
Δ = -112-4·1·(-840)
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-59}{2*1}=\frac{-48}{2}
=-24
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+59}{2*1}=\frac{70}{2}
=35
$