-10x^2=27x-18

Solution for -10x^2=27x-18 equation:

-10x^2=27x-18

We move all terms to the left:

-10x^2-(27x-18)=0

We get rid of parentheses

-10x^2-27x+18=0

a = -10; b = -27; c = +18;
Δ = b2-4ac
Δ = -272-4·(-10)·18
Δ = 1449
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:

$\sqrt{\Delta}=\sqrt{1449}=\sqrt{9*161}=\sqrt{9}*\sqrt{161}=3\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3\sqrt{161}}{2*-10}=\frac{27-3\sqrt{161}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3\sqrt{161}}{2*-10}=\frac{27+3\sqrt{161}}{-20}
$