4x2-10x+3=2x-5

Solution for 4x2-10x+3=2x-5 equation:

4x^2-10x+3=2x-5

We move all terms to the left:

4x^2-10x+3-(2x-5)=0

We get rid of parentheses

4x^2-10x-2x+5+3=0

We add all the numbers together, and all the variables

4x^2-12x+8=0

a = 4; b = -12; c = +8;
Δ = b2-4ac
Δ = -122-4·4·8
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4}{2*4}=\frac{8}{8}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4}{2*4}=\frac{16}{8}
=2
$