a^2-11a=7a+15

Solution for a^2-11a=7a+15 equation:

a^2-11a=7a+15

We move all terms to the left:

a^2-11a-(7a+15)=0

We get rid of parentheses

a^2-11a-7a-15=0

We add all the numbers together, and all the variables

a^2-18a-15=0

a = 1; b = -18; c = -15;
Δ = b2-4ac
Δ = -182-4·1·(-15)
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-8\sqrt{6}}{2*1}=\frac{18-8\sqrt{6}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+8\sqrt{6}}{2*1}=\frac{18+8\sqrt{6}}{2}
$