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x+4x(3x-7)-22=0
We multiply parentheses
12x^2+x-28x-22=0
We add all the numbers together, and all the variables
12x^2-27x-22=0
a = 12; b = -27; c = -22;
Δ = b2-4ac
Δ = -272-4·12·(-22)
Δ = 1785
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{-(-27)-\sqrt{1785}}{2*12}=\frac{27-\sqrt{1785}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{1785}}{2*12}=\frac{27+\sqrt{1785}}{24} $
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