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4x^2-3x-7=30x
We move all terms to the left:
4x^2-3x-7-(30x)=0
We add all the numbers together, and all the variables
4x^2-33x-7=0
a = 4; b = -33; c = -7;
Δ = b2-4ac
Δ = -332-4·4·(-7)
Δ = 1201
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{-(-33)-\sqrt{1201}}{2*4}=\frac{33-\sqrt{1201}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+\sqrt{1201}}{2*4}=\frac{33+\sqrt{1201}}{8} $
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