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(5x+2)(16x+10)=180
We move all terms to the left:
(5x+2)(16x+10)-(180)=0
We multiply parentheses ..
(+80x^2+50x+32x+20)-180=0
We get rid of parentheses
80x^2+50x+32x+20-180=0
We add all the numbers together, and all the variables
80x^2+82x-160=0
a = 80; b = 82; c = -160;
Δ = b2-4ac
Δ = 822-4·80·(-160)
Δ = 57924
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{57924}=\sqrt{36*1609}=\sqrt{36}*\sqrt{1609}=6\sqrt{1609}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(82)-6\sqrt{1609}}{2*80}=\frac{-82-6\sqrt{1609}}{160} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(82)+6\sqrt{1609}}{2*80}=\frac{-82+6\sqrt{1609}}{160} $
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