2x^2+5x^2=8x+20

Solution for 2x^2+5x^2=8x+20 equation:

2x^2+5x^2=8x+20

We move all terms to the left:

2x^2+5x^2-(8x+20)=0

We add all the numbers together, and all the variables

7x^2-(8x+20)=0

We get rid of parentheses

7x^2-8x-20=0

a = 7; b = -8; c = -20;
Δ = b2-4ac
Δ = -82-4·7·(-20)
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{39}}{2*7}=\frac{8-4\sqrt{39}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{39}}{2*7}=\frac{8+4\sqrt{39}}{14}
$