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12x^2-15x=19
We move all terms to the left:
12x^2-15x-(19)=0
a = 12; b = -15; c = -19;
Δ = b2-4ac
Δ = -152-4·12·(-19)
Δ = 1137
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{-(-15)-\sqrt{1137}}{2*12}=\frac{15-\sqrt{1137}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{1137}}{2*12}=\frac{15+\sqrt{1137}}{24} $
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