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12x(4x+16)+21=5x
We move all terms to the left:
12x(4x+16)+21-(5x)=0
We add all the numbers together, and all the variables
-5x+12x(4x+16)+21=0
We multiply parentheses
48x^2-5x+192x+21=0
We add all the numbers together, and all the variables
48x^2+187x+21=0
a = 48; b = 187; c = +21;
Δ = b2-4ac
Δ = 1872-4·48·21
Δ = 30937
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{-(187)-\sqrt{30937}}{2*48}=\frac{-187-\sqrt{30937}}{96} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(187)+\sqrt{30937}}{2*48}=\frac{-187+\sqrt{30937}}{96} $
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