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-9x^2=4x-19
We move all terms to the left:
-9x^2-(4x-19)=0
We get rid of parentheses
-9x^2-4x+19=0
a = -9; b = -4; c = +19;
Δ = b2-4ac
Δ = -42-4·(-9)·19
Δ = 700
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{700}=\sqrt{100*7}=\sqrt{100}*\sqrt{7}=10\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-10\sqrt{7}}{2*-9}=\frac{4-10\sqrt{7}}{-18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+10\sqrt{7}}{2*-9}=\frac{4+10\sqrt{7}}{-18} $
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