86=(3x-2)2+(2x)2

Solution for 86=(3x-2)2+(2x)2 equation:

86=(3x-2)2+(2x)2

We move all terms to the left:

86-((3x-2)2+(2x)2)=0


We calculate terms in parentheses: -((3x-2)2+2x2), so:

(3x-2)2+2x2

We add all the numbers together, and all the variables

2x^2+(3x-2)2

We multiply parentheses

2x^2+6x-4

Back to the equation:

-(2x^2+6x-4)


We get rid of parentheses

-2x^2-6x+4+86=0

We add all the numbers together, and all the variables

-2x^2-6x+90=0

a = -2; b = -6; c = +90;
Δ = b2-4ac
Δ = -62-4·(-2)·90
Δ = 756
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:

$\sqrt{\Delta}=\sqrt{756}=\sqrt{36*21}=\sqrt{36}*\sqrt{21}=6\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{21}}{2*-2}=\frac{6-6\sqrt{21}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{21}}{2*-2}=\frac{6+6\sqrt{21}}{-4}
$