4x^2+x^2=34^2

Solution for 4x^2+x^2=34^2 equation:

4x^2+x^2=34^2

We move all terms to the left:

4x^2+x^2-(34^2)=0

We add all the numbers together, and all the variables

5x^2-1156=0

a = 5; b = 0; c = -1156;
Δ = b2-4ac
Δ = 02-4·5·(-1156)
Δ = 23120
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:

$\sqrt{\Delta}=\sqrt{23120}=\sqrt{4624*5}=\sqrt{4624}*\sqrt{5}=68\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-68\sqrt{5}}{2*5}=\frac{0-68\sqrt{5}}{10}
=-\frac{68\sqrt{5}}{10}
=-\frac{34\sqrt{5}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+68\sqrt{5}}{2*5}=\frac{0+68\sqrt{5}}{10}
=\frac{68\sqrt{5}}{10}
=\frac{34\sqrt{5}}{5}
$