(6x+1)(5x+1)+90=180

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Solution for (6x+1)(5x+1)+90=180 equation:



(6x+1)(5x+1)+90=180
We move all terms to the left:
(6x+1)(5x+1)+90-(180)=0
We add all the numbers together, and all the variables
(6x+1)(5x+1)-90=0
We multiply parentheses ..
(+30x^2+6x+5x+1)-90=0
We get rid of parentheses
30x^2+6x+5x+1-90=0
We add all the numbers together, and all the variables
30x^2+11x-89=0
a = 30; b = 11; c = -89;
Δ = b2-4ac
Δ = 112-4·30·(-89)
Δ = 10801
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{-(11)-\sqrt{10801}}{2*30}=\frac{-11-\sqrt{10801}}{60} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{10801}}{2*30}=\frac{-11+\sqrt{10801}}{60} $

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