(6x)2+(7x+11)2=360

Solution for (6x)2+(7x+11)2=360 equation:

(6x)2+(7x+11)2=360

We move all terms to the left:

(6x)2+(7x+11)2-(360)=0

We add all the numbers together, and all the variables

6x^2+(7x+11)2-360=0

We multiply parentheses

6x^2+14x+22-360=0

We add all the numbers together, and all the variables

6x^2+14x-338=0

a = 6; b = 14; c = -338;
Δ = b2-4ac
Δ = 142-4·6·(-338)
Δ = 8308
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8308}=\sqrt{4*2077}=\sqrt{4}*\sqrt{2077}=2\sqrt{2077}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{2077}}{2*6}=\frac{-14-2\sqrt{2077}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{2077}}{2*6}=\frac{-14+2\sqrt{2077}}{12}
$