(3x+25)(5x-7)=180

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Solution for (3x+25)(5x-7)=180 equation:



(3x+25)(5x-7)=180
We move all terms to the left:
(3x+25)(5x-7)-(180)=0
We multiply parentheses ..
(+15x^2-21x+125x-175)-180=0
We get rid of parentheses
15x^2-21x+125x-175-180=0
We add all the numbers together, and all the variables
15x^2+104x-355=0
a = 15; b = 104; c = -355;
Δ = b2-4ac
Δ = 1042-4·15·(-355)
Δ = 32116
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:
$\sqrt{\Delta}=\sqrt{32116}=\sqrt{4*8029}=\sqrt{4}*\sqrt{8029}=2\sqrt{8029}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(104)-2\sqrt{8029}}{2*15}=\frac{-104-2\sqrt{8029}}{30} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(104)+2\sqrt{8029}}{2*15}=\frac{-104+2\sqrt{8029}}{30} $

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