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4x^2=27x-7
We move all terms to the left:
4x^2-(27x-7)=0
We get rid of parentheses
4x^2-27x+7=0
a = 4; b = -27; c = +7;
Δ = b2-4ac
Δ = -272-4·4·7
Δ = 617
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{617}}{2*4}=\frac{27-\sqrt{617}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{617}}{2*4}=\frac{27+\sqrt{617}}{8} $
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