6x^2+7x^2-20=0

Solution for 6x^2+7x^2-20=0 equation:

6x^2+7x^2-20=0

We add all the numbers together, and all the variables

13x^2-20=0

a = 13; b = 0; c = -20;
Δ = b2-4ac
Δ = 02-4·13·(-20)
Δ = 1040
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:

$\sqrt{\Delta}=\sqrt{1040}=\sqrt{16*65}=\sqrt{16}*\sqrt{65}=4\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{65}}{2*13}=\frac{0-4\sqrt{65}}{26}
=-\frac{4\sqrt{65}}{26}
=-\frac{2\sqrt{65}}{13}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{65}}{2*13}=\frac{0+4\sqrt{65}}{26}
=\frac{4\sqrt{65}}{26}
=\frac{2\sqrt{65}}{13}
$