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(4x+7)(x-3)-(12x+21)=0
We get rid of parentheses
(4x+7)(x-3)-12x-21=0
We multiply parentheses ..
(+4x^2-12x+7x-21)-12x-21=0
We get rid of parentheses
4x^2-12x+7x-12x-21-21=0
We add all the numbers together, and all the variables
4x^2-17x-42=0
a = 4; b = -17; c = -42;
Δ = b2-4ac
Δ = -172-4·4·(-42)
Δ = 961
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{961}=31$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-31}{2*4}=\frac{-14}{8} =-1+3/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+31}{2*4}=\frac{48}{8} =6 $
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