(x^2/36)+4x+64=0

Solution for (x^2/36)+4x+64=0 equation:

(x^2/36)+4x+64=0

We add all the numbers together, and all the variables

4x+(x^2/36)+64=0

We get rid of parentheses

x^2/36+4x+64=0

We multiply all the terms by the denominator


x^2+4x*36+64*36=0

We add all the numbers together, and all the variables

x^2+4x*36+2304=0

Wy multiply elements

x^2+144x+2304=0

a = 1; b = 144; c = +2304;
Δ = b2-4ac
Δ = 1442-4·1·2304
Δ = 11520
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:

$\sqrt{\Delta}=\sqrt{11520}=\sqrt{2304*5}=\sqrt{2304}*\sqrt{5}=48\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-48\sqrt{5}}{2*1}=\frac{-144-48\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+48\sqrt{5}}{2*1}=\frac{-144+48\sqrt{5}}{2}
$