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(3x+25)(3x+85)+4x=360
We move all terms to the left:
(3x+25)(3x+85)+4x-(360)=0
We add all the numbers together, and all the variables
4x+(3x+25)(3x+85)-360=0
We multiply parentheses ..
(+9x^2+255x+75x+2125)+4x-360=0
We get rid of parentheses
9x^2+255x+75x+4x+2125-360=0
We add all the numbers together, and all the variables
9x^2+334x+1765=0
a = 9; b = 334; c = +1765;
Δ = b2-4ac
Δ = 3342-4·9·1765
Δ = 48016
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{48016}=\sqrt{16*3001}=\sqrt{16}*\sqrt{3001}=4\sqrt{3001}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(334)-4\sqrt{3001}}{2*9}=\frac{-334-4\sqrt{3001}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(334)+4\sqrt{3001}}{2*9}=\frac{-334+4\sqrt{3001}}{18} $
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