5x^2+10x-9=3x-3

Solution for 5x^2+10x-9=3x-3 equation:

5x^2+10x-9=3x-3

We move all terms to the left:

5x^2+10x-9-(3x-3)=0

We get rid of parentheses

5x^2+10x-3x+3-9=0

We add all the numbers together, and all the variables

5x^2+7x-6=0

a = 5; b = 7; c = -6;
Δ = b2-4ac
Δ = 72-4·5·(-6)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-13}{2*5}=\frac{-20}{10}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+13}{2*5}=\frac{6}{10}
=3/5
$