10x^2-60x+45=45-30x

Solution for 10x^2-60x+45=45-30x equation:

10x^2-60x+45=45-30x

We move all terms to the left:

10x^2-60x+45-(45-30x)=0

We add all the numbers together, and all the variables

10x^2-60x-(-30x+45)+45=0

We get rid of parentheses

10x^2-60x+30x-45+45=0

We add all the numbers together, and all the variables

10x^2-30x=0

a = 10; b = -30; c = 0;
Δ = b2-4ac
Δ = -302-4·10·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-30}{2*10}=\frac{0}{20}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+30}{2*10}=\frac{60}{20}
=3
$