9x+10x^2=2x^2-5x

Solution for 9x+10x^2=2x^2-5x equation:

9x+10x^2=2x^2-5x

We move all terms to the left:

9x+10x^2-(2x^2-5x)=0

We get rid of parentheses

10x^2-2x^2+9x+5x=0

We add all the numbers together, and all the variables

8x^2+14x=0

a = 8; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·8·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*8}=\frac{-28}{16}
=-1+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*8}=\frac{0}{16}
=0
$