7x^2+x^2=113

Solution for 7x^2+x^2=113 equation:

7x^2+x^2=113

We move all terms to the left:

7x^2+x^2-(113)=0

We add all the numbers together, and all the variables

8x^2-113=0

a = 8; b = 0; c = -113;
Δ = b2-4ac
Δ = 02-4·8·(-113)
Δ = 3616
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:

$\sqrt{\Delta}=\sqrt{3616}=\sqrt{16*226}=\sqrt{16}*\sqrt{226}=4\sqrt{226}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{226}}{2*8}=\frac{0-4\sqrt{226}}{16}
=-\frac{4\sqrt{226}}{16}
=-\frac{\sqrt{226}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{226}}{2*8}=\frac{0+4\sqrt{226}}{16}
=\frac{4\sqrt{226}}{16}
=\frac{\sqrt{226}}{4}
$