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15x-10=-9x^2
We move all terms to the left:
15x-10-(-9x^2)=0
We get rid of parentheses
9x^2+15x-10=0
a = 9; b = 15; c = -10;
Δ = b2-4ac
Δ = 152-4·9·(-10)
Δ = 585
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{65}}{2*9}=\frac{-15-3\sqrt{65}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{65}}{2*9}=\frac{-15+3\sqrt{65}}{18} $
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