10x^2=45x-45

Solution for 10x^2=45x-45 equation:

10x^2=45x-45

We move all terms to the left:

10x^2-(45x-45)=0

We get rid of parentheses

10x^2-45x+45=0

a = 10; b = -45; c = +45;
Δ = b2-4ac
Δ = -452-4·10·45
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-15}{2*10}=\frac{30}{20}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+15}{2*10}=\frac{60}{20}
=3
$