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(3x+16)(4x-7)=180
We move all terms to the left:
(3x+16)(4x-7)-(180)=0
We multiply parentheses ..
(+12x^2-21x+64x-112)-180=0
We get rid of parentheses
12x^2-21x+64x-112-180=0
We add all the numbers together, and all the variables
12x^2+43x-292=0
a = 12; b = 43; c = -292;
Δ = b2-4ac
Δ = 432-4·12·(-292)
Δ = 15865
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(43)-\sqrt{15865}}{2*12}=\frac{-43-\sqrt{15865}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+\sqrt{15865}}{2*12}=\frac{-43+\sqrt{15865}}{24} $
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