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5x(3x-7)=8
We move all terms to the left:
5x(3x-7)-(8)=0
We multiply parentheses
15x^2-35x-8=0
a = 15; b = -35; c = -8;
Δ = b2-4ac
Δ = -352-4·15·(-8)
Δ = 1705
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{-(-35)-\sqrt{1705}}{2*15}=\frac{35-\sqrt{1705}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{1705}}{2*15}=\frac{35+\sqrt{1705}}{30} $
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