(3x-10+)(2x+30)=180

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Solution for (3x-10+)(2x+30)=180 equation:



(3x-10+)(2x+30)=180
We move all terms to the left:
(3x-10+)(2x+30)-(180)=0
We add all the numbers together, and all the variables
(+3x)(2x+30)-180=0
We multiply parentheses ..
(+6x^2+90x)-180=0
We get rid of parentheses
6x^2+90x-180=0
a = 6; b = 90; c = -180;
Δ = b2-4ac
Δ = 902-4·6·(-180)
Δ = 12420
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:
$\sqrt{\Delta}=\sqrt{12420}=\sqrt{36*345}=\sqrt{36}*\sqrt{345}=6\sqrt{345}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-6\sqrt{345}}{2*6}=\frac{-90-6\sqrt{345}}{12} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+6\sqrt{345}}{2*6}=\frac{-90+6\sqrt{345}}{12} $

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