4x^2=-5x+51

Solution for 4x^2=-5x+51 equation:

4x^2=-5x+51

We move all terms to the left:

4x^2-(-5x+51)=0

We get rid of parentheses

4x^2+5x-51=0

a = 4; b = 5; c = -51;
Δ = b2-4ac
Δ = 52-4·4·(-51)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-29}{2*4}=\frac{-34}{8}
=-4+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+29}{2*4}=\frac{24}{8}
=3
$