3/5x^2+7=88

Solution for 3/5x^2+7=88 equation:

3/5x^2+7=88

We move all terms to the left:

3/5x^2+7-(88)=0


Domain of the equation: 5x^2!=0

x^2!=0/5

x^2!=√0

x!=0

x∈R


We add all the numbers together, and all the variables

3/5x^2-81=0

We multiply all the terms by the denominator


-81*5x^2+3=0

Wy multiply elements

-405x^2+3=0

a = -405; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-405)·3
Δ = 4860
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:

$\sqrt{\Delta}=\sqrt{4860}=\sqrt{324*15}=\sqrt{324}*\sqrt{15}=18\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{15}}{2*-405}=\frac{0-18\sqrt{15}}{-810}
=-\frac{18\sqrt{15}}{-810}
=-\frac{\sqrt{15}}{-45}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{15}}{2*-405}=\frac{0+18\sqrt{15}}{-810}
=\frac{18\sqrt{15}}{-810}
=\frac{\sqrt{15}}{-45}
$