((2x*2x)+90)=(x*x+115)

Solution for ((2x*2x)+90)=(x*x+115) equation:

((2x*2x)+90)=(x*x+115)

We move all terms to the left:

((2x*2x)+90)-((x*x+115))=0

We add all the numbers together, and all the variables

((+2x*2x)+90)-((x*x+115))=0


We calculate terms in parentheses: +((+2x*2x)+90), so:

(+2x*2x)+90

We get rid of parentheses

2x*2x+90

Wy multiply elements

4x^2+90

Back to the equation:

+(4x^2+90)



We calculate terms in parentheses: -((x*x+115)), so:

(x*x+115)

We get rid of parentheses

x*x+115

Wy multiply elements

x^2+115

Back to the equation:

-(x^2+115)


We get rid of parentheses

4x^2-x^2+90-115=0

We add all the numbers together, and all the variables

3x^2-25=0

a = 3; b = 0; c = -25;
Δ = b2-4ac
Δ = 02-4·3·(-25)
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{3}}{2*3}=\frac{0-10\sqrt{3}}{6}
=-\frac{10\sqrt{3}}{6}
=-\frac{5\sqrt{3}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{3}}{2*3}=\frac{0+10\sqrt{3}}{6}
=\frac{10\sqrt{3}}{6}
=\frac{5\sqrt{3}}{3}
$