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(10x+5)(12x-1)=180
We move all terms to the left:
(10x+5)(12x-1)-(180)=0
We multiply parentheses ..
(+120x^2-10x+60x-5)-180=0
We get rid of parentheses
120x^2-10x+60x-5-180=0
We add all the numbers together, and all the variables
120x^2+50x-185=0
a = 120; b = 50; c = -185;
Δ = b2-4ac
Δ = 502-4·120·(-185)
Δ = 91300
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{91300}=\sqrt{100*913}=\sqrt{100}*\sqrt{913}=10\sqrt{913}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-10\sqrt{913}}{2*120}=\frac{-50-10\sqrt{913}}{240} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+10\sqrt{913}}{2*120}=\frac{-50+10\sqrt{913}}{240} $
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