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4x^2-11x=7
We move all terms to the left:
4x^2-11x-(7)=0
a = 4; b = -11; c = -7;
Δ = b2-4ac
Δ = -112-4·4·(-7)
Δ = 233
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{-(-11)-\sqrt{233}}{2*4}=\frac{11-\sqrt{233}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{233}}{2*4}=\frac{11+\sqrt{233}}{8} $
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