10-1/4x2=-7

Solution for 10-1/4x2=-7 equation:

10-1/4x^2=-7

We move all terms to the left:

10-1/4x^2-(-7)=0


Domain of the equation: 4x^2!=0

x^2!=0/4

x^2!=√0

x!=0

x∈R


We add all the numbers together, and all the variables

-1/4x^2+17=0

We multiply all the terms by the denominator


17*4x^2-1=0

Wy multiply elements

68x^2-1=0

a = 68; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·68·(-1)
Δ = 272
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:

$\sqrt{\Delta}=\sqrt{272}=\sqrt{16*17}=\sqrt{16}*\sqrt{17}=4\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{17}}{2*68}=\frac{0-4\sqrt{17}}{136}
=-\frac{4\sqrt{17}}{136}
=-\frac{\sqrt{17}}{34}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{17}}{2*68}=\frac{0+4\sqrt{17}}{136}
=\frac{4\sqrt{17}}{136}
=\frac{\sqrt{17}}{34}
$