20x^2-105x-143=2x^2+4

Solution for 20x^2-105x-143=2x^2+4 equation:

20x^2-105x-143=2x^2+4

We move all terms to the left:

20x^2-105x-143-(2x^2+4)=0

We get rid of parentheses

20x^2-2x^2-105x-4-143=0

We add all the numbers together, and all the variables

18x^2-105x-147=0

a = 18; b = -105; c = -147;
Δ = b2-4ac
Δ = -1052-4·18·(-147)
Δ = 21609
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{21609}=147$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-105)-147}{2*18}=\frac{-42}{36}
=-1+1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+147}{2*18}=\frac{252}{36}
=7
$