-9x2/10=-19

Solution for -9x2/10=-19 equation:

-9x^2/10=-19

We move all terms to the left:

-9x^2/10-(-19)=0

We add all the numbers together, and all the variables

-9x^2/10+19=0

We multiply all the terms by the denominator


-9x^2+19*10=0

We add all the numbers together, and all the variables

-9x^2+190=0

a = -9; b = 0; c = +190;
Δ = b2-4ac
Δ = 02-4·(-9)·190
Δ = 6840
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:

$\sqrt{\Delta}=\sqrt{6840}=\sqrt{36*190}=\sqrt{36}*\sqrt{190}=6\sqrt{190}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{190}}{2*-9}=\frac{0-6\sqrt{190}}{-18}
=-\frac{6\sqrt{190}}{-18}
=-\frac{\sqrt{190}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{190}}{2*-9}=\frac{0+6\sqrt{190}}{-18}
=\frac{6\sqrt{190}}{-18}
=\frac{\sqrt{190}}{-3}
$