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(5x-12)(2x+1)=16
We move all terms to the left:
(5x-12)(2x+1)-(16)=0
We multiply parentheses ..
(+10x^2+5x-24x-12)-16=0
We get rid of parentheses
10x^2+5x-24x-12-16=0
We add all the numbers together, and all the variables
10x^2-19x-28=0
a = 10; b = -19; c = -28;
Δ = b2-4ac
Δ = -192-4·10·(-28)
Δ = 1481
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{-(-19)-\sqrt{1481}}{2*10}=\frac{19-\sqrt{1481}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{1481}}{2*10}=\frac{19+\sqrt{1481}}{20} $
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