7x(18x-20)=(8x+2)

Solution for 7x(18x-20)=(8x+2) equation:

7x(18x-20)=(8x+2)

We move all terms to the left:

7x(18x-20)-((8x+2))=0

We multiply parentheses

126x^2-140x-((8x+2))=0


We calculate terms in parentheses: -((8x+2)), so:

(8x+2)

We get rid of parentheses

8x+2

Back to the equation:

-(8x+2)


We get rid of parentheses

126x^2-140x-8x-2=0

We add all the numbers together, and all the variables

126x^2-148x-2=0

a = 126; b = -148; c = -2;
Δ = b2-4ac
Δ = -1482-4·126·(-2)
Δ = 22912
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:

$\sqrt{\Delta}=\sqrt{22912}=\sqrt{64*358}=\sqrt{64}*\sqrt{358}=8\sqrt{358}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-148)-8\sqrt{358}}{2*126}=\frac{148-8\sqrt{358}}{252}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-148)+8\sqrt{358}}{2*126}=\frac{148+8\sqrt{358}}{252}
$