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(15x+7)(29x-3)=180
We move all terms to the left:
(15x+7)(29x-3)-(180)=0
We multiply parentheses ..
(+435x^2-45x+203x-21)-180=0
We get rid of parentheses
435x^2-45x+203x-21-180=0
We add all the numbers together, and all the variables
435x^2+158x-201=0
a = 435; b = 158; c = -201;
Δ = b2-4ac
Δ = 1582-4·435·(-201)
Δ = 374704
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{374704}=\sqrt{16*23419}=\sqrt{16}*\sqrt{23419}=4\sqrt{23419}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(158)-4\sqrt{23419}}{2*435}=\frac{-158-4\sqrt{23419}}{870} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(158)+4\sqrt{23419}}{2*435}=\frac{-158+4\sqrt{23419}}{870} $
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