4x2-31x+49=-3x+4

Solution for 4x2-31x+49=-3x+4 equation:

4x^2-31x+49=-3x+4

We move all terms to the left:

4x^2-31x+49-(-3x+4)=0

We get rid of parentheses

4x^2-31x+3x-4+49=0

We add all the numbers together, and all the variables

4x^2-28x+45=0

a = 4; b = -28; c = +45;
Δ = b2-4ac
Δ = -282-4·4·45
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-8}{2*4}=\frac{20}{8}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+8}{2*4}=\frac{36}{8}
=4+1/2
$