1=10x2+9x

Solution for 1=10x2+9x equation:

1=10x^2+9x

We move all terms to the left:

1-(10x^2+9x)=0

We get rid of parentheses

-10x^2-9x+1=0

a = -10; b = -9; c = +1;
Δ = b2-4ac
Δ = -92-4·(-10)·1
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-11}{2*-10}=\frac{-2}{-20}
=1/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+11}{2*-10}=\frac{20}{-20}
=-1
$