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4x(4x+3)=19x+9-3x+3
We move all terms to the left:
4x(4x+3)-(19x+9-3x+3)=0
We add all the numbers together, and all the variables
4x(4x+3)-(16x+12)=0
We multiply parentheses
16x^2+12x-(16x+12)=0
We get rid of parentheses
16x^2+12x-16x-12=0
We add all the numbers together, and all the variables
16x^2-4x-12=0
a = 16; b = -4; c = -12;
Δ = b2-4ac
Δ = -42-4·16·(-12)
Δ = 784
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{784}=28$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-28}{2*16}=\frac{-24}{32} =-3/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+28}{2*16}=\frac{32}{32} =1 $
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