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(4x+5)(12x+5)=180
We move all terms to the left:
(4x+5)(12x+5)-(180)=0
We multiply parentheses ..
(+48x^2+20x+60x+25)-180=0
We get rid of parentheses
48x^2+20x+60x+25-180=0
We add all the numbers together, and all the variables
48x^2+80x-155=0
a = 48; b = 80; c = -155;
Δ = b2-4ac
Δ = 802-4·48·(-155)
Δ = 36160
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{36160}=\sqrt{64*565}=\sqrt{64}*\sqrt{565}=8\sqrt{565}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-8\sqrt{565}}{2*48}=\frac{-80-8\sqrt{565}}{96} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+8\sqrt{565}}{2*48}=\frac{-80+8\sqrt{565}}{96} $
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