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-3x(4x+5)+4x+1=-30
We move all terms to the left:
-3x(4x+5)+4x+1-(-30)=0
We add all the numbers together, and all the variables
4x-3x(4x+5)+31=0
We multiply parentheses
-12x^2+4x-15x+31=0
We add all the numbers together, and all the variables
-12x^2-11x+31=0
a = -12; b = -11; c = +31;
Δ = b2-4ac
Δ = -112-4·(-12)·31
Δ = 1609
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{-(-11)-\sqrt{1609}}{2*-12}=\frac{11-\sqrt{1609}}{-24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{1609}}{2*-12}=\frac{11+\sqrt{1609}}{-24} $
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