3x^2+5=5x^2-8x

Solution for 3x^2+5=5x^2-8x equation:

3x^2+5=5x^2-8x

We move all terms to the left:

3x^2+5-(5x^2-8x)=0

We get rid of parentheses

3x^2-5x^2+8x+5=0

We add all the numbers together, and all the variables

-2x^2+8x+5=0

a = -2; b = 8; c = +5;
Δ = b2-4ac
Δ = 82-4·(-2)·5
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{26}}{2*-2}=\frac{-8-2\sqrt{26}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{26}}{2*-2}=\frac{-8+2\sqrt{26}}{-4}
$