4x^2-10x-6=10

Solution for 4x^2-10x-6=10 equation:

4x^2-10x-6=10

We move all terms to the left:

4x^2-10x-6-(10)=0

We add all the numbers together, and all the variables

4x^2-10x-16=0

a = 4; b = -10; c = -16;
Δ = b2-4ac
Δ = -102-4·4·(-16)
Δ = 356
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:

$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{89}}{2*4}=\frac{10-2\sqrt{89}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{89}}{2*4}=\frac{10+2\sqrt{89}}{8}
$