21x^2=59x-36

Solution for 21x^2=59x-36 equation:

21x^2=59x-36

We move all terms to the left:

21x^2-(59x-36)=0

We get rid of parentheses

21x^2-59x+36=0

a = 21; b = -59; c = +36;
Δ = b2-4ac
Δ = -592-4·21·36
Δ = 457
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-59)-\sqrt{457}}{2*21}=\frac{59-\sqrt{457}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+\sqrt{457}}{2*21}=\frac{59+\sqrt{457}}{42}
$