10x^2-8x-55=7

Solution for 10x^2-8x-55=7 equation:

10x^2-8x-55=7

We move all terms to the left:

10x^2-8x-55-(7)=0

We add all the numbers together, and all the variables

10x^2-8x-62=0

a = 10; b = -8; c = -62;
Δ = b2-4ac
Δ = -82-4·10·(-62)
Δ = 2544
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:

$\sqrt{\Delta}=\sqrt{2544}=\sqrt{16*159}=\sqrt{16}*\sqrt{159}=4\sqrt{159}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{159}}{2*10}=\frac{8-4\sqrt{159}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{159}}{2*10}=\frac{8+4\sqrt{159}}{20}
$