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(7x+12)(4x+3)=180
We move all terms to the left:
(7x+12)(4x+3)-(180)=0
We multiply parentheses ..
(+28x^2+21x+48x+36)-180=0
We get rid of parentheses
28x^2+21x+48x+36-180=0
We add all the numbers together, and all the variables
28x^2+69x-144=0
a = 28; b = 69; c = -144;
Δ = b2-4ac
Δ = 692-4·28·(-144)
Δ = 20889
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{20889}=\sqrt{9*2321}=\sqrt{9}*\sqrt{2321}=3\sqrt{2321}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(69)-3\sqrt{2321}}{2*28}=\frac{-69-3\sqrt{2321}}{56} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(69)+3\sqrt{2321}}{2*28}=\frac{-69+3\sqrt{2321}}{56} $
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