180=(6x-1)(5x+13)+58

Solution for 180=(6x-1)(5x+13)+58 equation:

180=(6x-1)(5x+13)+58

We move all terms to the left:

180-((6x-1)(5x+13)+58)=0

We multiply parentheses ..

-((+30x^2+78x-5x-13)+58)+180=0


We calculate terms in parentheses: -((+30x^2+78x-5x-13)+58), so:

(+30x^2+78x-5x-13)+58

We get rid of parentheses

30x^2+78x-5x-13+58

We add all the numbers together, and all the variables

30x^2+73x+45

Back to the equation:

-(30x^2+73x+45)


We get rid of parentheses

-30x^2-73x-45+180=0

We add all the numbers together, and all the variables

-30x^2-73x+135=0

a = -30; b = -73; c = +135;
Δ = b2-4ac
Δ = -732-4·(-30)·135
Δ = 21529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-73)-\sqrt{21529}}{2*-30}=\frac{73-\sqrt{21529}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-73)+\sqrt{21529}}{2*-30}=\frac{73+\sqrt{21529}}{-60}
$