3x^2+4x^2=35^2

Solution for 3x^2+4x^2=35^2 equation:

3x^2+4x^2=35^2

We move all terms to the left:

3x^2+4x^2-(35^2)=0

We add all the numbers together, and all the variables

7x^2-1225=0

a = 7; b = 0; c = -1225;
Δ = b2-4ac
Δ = 02-4·7·(-1225)
Δ = 34300
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:

$\sqrt{\Delta}=\sqrt{34300}=\sqrt{4900*7}=\sqrt{4900}*\sqrt{7}=70\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-70\sqrt{7}}{2*7}=\frac{0-70\sqrt{7}}{14}
=-\frac{70\sqrt{7}}{14}
=-5\sqrt{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+70\sqrt{7}}{2*7}=\frac{0+70\sqrt{7}}{14}
=\frac{70\sqrt{7}}{14}
=5\sqrt{7}
$