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7x(2x-27)=8
We move all terms to the left:
7x(2x-27)-(8)=0
We multiply parentheses
14x^2-189x-8=0
a = 14; b = -189; c = -8;
Δ = b2-4ac
Δ = -1892-4·14·(-8)
Δ = 36169
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{-(-189)-\sqrt{36169}}{2*14}=\frac{189-\sqrt{36169}}{28} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-189)+\sqrt{36169}}{2*14}=\frac{189+\sqrt{36169}}{28} $
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