4x^2-3x-10=12

Solution for 4x^2-3x-10=12 equation:

4x^2-3x-10=12

We move all terms to the left:

4x^2-3x-10-(12)=0

We add all the numbers together, and all the variables

4x^2-3x-22=0

a = 4; b = -3; c = -22;
Δ = b2-4ac
Δ = -32-4·4·(-22)
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{-(-3)-19}{2*4}=\frac{-16}{8}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+19}{2*4}=\frac{22}{8}
=2+3/4
$