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4(2x-7)(4x+3)=112
We move all terms to the left:
4(2x-7)(4x+3)-(112)=0
We multiply parentheses ..
4(+8x^2+6x-28x-21)-112=0
We multiply parentheses
32x^2+24x-112x-84-112=0
We add all the numbers together, and all the variables
32x^2-88x-196=0
a = 32; b = -88; c = -196;
Δ = b2-4ac
Δ = -882-4·32·(-196)
Δ = 32832
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{32832}=\sqrt{576*57}=\sqrt{576}*\sqrt{57}=24\sqrt{57}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88)-24\sqrt{57}}{2*32}=\frac{88-24\sqrt{57}}{64} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88)+24\sqrt{57}}{2*32}=\frac{88+24\sqrt{57}}{64} $
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