4x2=-10x+14

Solution for 4x2=-10x+14 equation:

4x^2=-10x+14

We move all terms to the left:

4x^2-(-10x+14)=0

We get rid of parentheses

4x^2+10x-14=0

a = 4; b = 10; c = -14;
Δ = b2-4ac
Δ = 102-4·4·(-14)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-18}{2*4}=\frac{-28}{8}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+18}{2*4}=\frac{8}{8}
=1
$