10x^2=35x-30

Solution for 10x^2=35x-30 equation:

10x^2=35x-30

We move all terms to the left:

10x^2-(35x-30)=0

We get rid of parentheses

10x^2-35x+30=0

a = 10; b = -35; c = +30;
Δ = b2-4ac
Δ = -352-4·10·30
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-5}{2*10}=\frac{30}{20}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+5}{2*10}=\frac{40}{20}
=2
$