6x^2-7x-3=10

Solution for 6x^2-7x-3=10 equation:

6x^2-7x-3=10

We move all terms to the left:

6x^2-7x-3-(10)=0

We add all the numbers together, and all the variables

6x^2-7x-13=0

a = 6; b = -7; c = -13;
Δ = b2-4ac
Δ = -72-4·6·(-13)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-19}{2*6}=\frac{-12}{12}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+19}{2*6}=\frac{26}{12}
=2+1/6
$