3x-2=5X^2-13x

Solution for 3x-2=5X^2-13x equation:

3x-2=5x^2-13x

We move all terms to the left:

3x-2-(5x^2-13x)=0

We get rid of parentheses

-5x^2+3x+13x-2=0

We add all the numbers together, and all the variables

-5x^2+16x-2=0

a = -5; b = 16; c = -2;
Δ = b2-4ac
Δ = 162-4·(-5)·(-2)
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-6\sqrt{6}}{2*-5}=\frac{-16-6\sqrt{6}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+6\sqrt{6}}{2*-5}=\frac{-16+6\sqrt{6}}{-10}
$