2-5x2-5x=3x-33x-3

Solution for 2-5x2-5x=3x-33x-3 equation:

2-5x^2-5x=3x-33x-3

We move all terms to the left:

2-5x^2-5x-(3x-33x-3)=0

We add all the numbers together, and all the variables

-5x^2-5x-(-30x-3)+2=0

We get rid of parentheses

-5x^2-5x+30x+3+2=0

We add all the numbers together, and all the variables

-5x^2+25x+5=0

a = -5; b = 25; c = +5;
Δ = b2-4ac
Δ = 252-4·(-5)·5
Δ = 725
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:

$\sqrt{\Delta}=\sqrt{725}=\sqrt{25*29}=\sqrt{25}*\sqrt{29}=5\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-5\sqrt{29}}{2*-5}=\frac{-25-5\sqrt{29}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+5\sqrt{29}}{2*-5}=\frac{-25+5\sqrt{29}}{-10}
$