6x^2-2x+5x-3=0

Solution for 6x^2-2x+5x-3=0 equation:

6x^2-2x+5x-3=0

We add all the numbers together, and all the variables

6x^2+3x-3=0

a = 6; b = 3; c = -3;
Δ = b2-4ac
Δ = 32-4·6·(-3)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-9}{2*6}=\frac{-12}{12}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+9}{2*6}=\frac{6}{12}
=1/2
$