(3+5x+x^2)-(8x^2-9x)=0

Solution for (3+5x+x^2)-(8x^2-9x)=0 equation:

(3+5x+x^2)-(8x^2-9x)=0

We get rid of parentheses

x^2-8x^2+5x+9x+3=0

We add all the numbers together, and all the variables

-7x^2+14x+3=0

a = -7; b = 14; c = +3;
Δ = b2-4ac
Δ = 142-4·(-7)·3
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{70}}{2*-7}=\frac{-14-2\sqrt{70}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{70}}{2*-7}=\frac{-14+2\sqrt{70}}{-14}
$