5x^2=30x-40

Solution for 5x^2=30x-40 equation:

5x^2=30x-40

We move all terms to the left:

5x^2-(30x-40)=0

We get rid of parentheses

5x^2-30x+40=0

a = 5; b = -30; c = +40;
Δ = b2-4ac
Δ = -302-4·5·40
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-10}{2*5}=\frac{20}{10}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+10}{2*5}=\frac{40}{10}
=4
$