4a^2-11a=7

Solution for 4a^2-11a=7 equation:

4a^2-11a=7

We move all terms to the left:

4a^2-11a-(7)=0

a = 4; b = -11; c = -7;
Δ = b2-4ac
Δ = -112-4·4·(-7)
Δ = 233
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{233}}{2*4}=\frac{11-\sqrt{233}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{233}}{2*4}=\frac{11+\sqrt{233}}{8}
$