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(3x-10)(5x+40)=180
We move all terms to the left:
(3x-10)(5x+40)-(180)=0
We multiply parentheses ..
(+15x^2+120x-50x-400)-180=0
We get rid of parentheses
15x^2+120x-50x-400-180=0
We add all the numbers together, and all the variables
15x^2+70x-580=0
a = 15; b = 70; c = -580;
Δ = b2-4ac
Δ = 702-4·15·(-580)
Δ = 39700
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{39700}=\sqrt{100*397}=\sqrt{100}*\sqrt{397}=10\sqrt{397}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-10\sqrt{397}}{2*15}=\frac{-70-10\sqrt{397}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+10\sqrt{397}}{2*15}=\frac{-70+10\sqrt{397}}{30} $
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