(6x-4)(10x+1)+77=180

Solution for (6x-4)(10x+1)+77=180 equation:

(6x-4)(10x+1)+77=180

We move all terms to the left:

(6x-4)(10x+1)+77-(180)=0

We add all the numbers together, and all the variables

(6x-4)(10x+1)-103=0

We multiply parentheses ..

(+60x^2+6x-40x-4)-103=0

We get rid of parentheses

60x^2+6x-40x-4-103=0

We add all the numbers together, and all the variables

60x^2-34x-107=0

a = 60; b = -34; c = -107;
Δ = b2-4ac
Δ = -342-4·60·(-107)
Δ = 26836
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:

$\sqrt{\Delta}=\sqrt{26836}=\sqrt{4*6709}=\sqrt{4}*\sqrt{6709}=2\sqrt{6709}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{6709}}{2*60}=\frac{34-2\sqrt{6709}}{120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{6709}}{2*60}=\frac{34+2\sqrt{6709}}{120}
$